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text: 4 Γ at zero momentum. On the other hand, for t = 0, 1 the model turns into two decoupled triangular lattices, The Hamilto(cid:16)nian (5) then turns into (cid:17) and we expect separate condensation of bosons on two √ sublattices. (cid:18) (cid:19) H ≈ − † † To study the possible condensates at ﬁnite values of t 3 3t ˆb (K )ˆb (K ) + ˆb (K )ˆb (K ) 1 2 A A A A B B B B and t , let us focus on the non–interacting Hamiltonian. The e2nergy dispersion of the lowest band (cid:15)−(k) √exhibits + U b† (K )ˆb (K ) (cid:18) 2 b† (K )ˆb (K ) − 1 (cid:19) 2 A A A A N A A A A either a single minimum at k = Γ for t > 3t or sites 1 2 degenerate minima at the two inequiva√lent corners of the U(cid:16)† 2 † (cid:17) − + b (K )ˆb (K ) b (K )ˆb (K ) 1 Brillouin zone KA and KB for t1 < 3t2 [see Fig. 1e)- 2 B B B B Nsites B B B B g)]. The momenta at the corners of the Brillouin zone − † † µ ˆb (K )ˆb (K ) + ˆb (K )ˆb (K ) , (15) satisfy A A A A B B B B · · − eiKA bi = ei23π , eiKB bi = e i23π , (9) i.e. it describes two decoupled sublattices since the nearest–neighbor tunneling term vanishes (cid:88) (cid:88) (cid:88) for all i = 1, 2, 3. At these high symmetry points, the Hamiltonian takes the following forms: † ∝ † 3 − · ˆbiˆbj ˆbi e iKB (ri+aj)ˆbB(KB) = 0. (16) H − (cid:104) (cid:105) i,j i j=1 (Γ) = 3t σ (10) 1 x Thus we conclude that the ground state consists of and two decoupled superﬂuids. The same observation follows √ directly from Eq. (12), i. e. at the mean–ﬁeld level the H ± ground–state consists of two separate condensates occu- (KA,B) = 3 3t2σz. (11) p(cid:0)ying the two subla(cid:1)ttices. √ Th√e mean-ﬁeld ground state energy (12) is E0 = ordTehrepSaFrapmheatseer fiosrm(cid:104)ˆbsi(cid:105)w=hen√tn1,>whe3rte2.nTh=e Nco/nNdesintessaties d−ist3rib3utt2inon+s 12aUren2ρ (akn)d≈thNe cδorres,poρnd(ikn)g ≈moNmNsδeitnetsum. the ﬁlling. The ground state energy obtained from the A 2 k,KA B 2 k,KB For the operators ˆb on the same sublattice we ﬁnd Gross–Pitaevskii (G(cid:88)P) energy functio(cid:88)nal [98] A,i from Eq. (9) (cid:88) − ∗ 1 | | E(cid:0)0 = i,j tijψi ψ(cid:1)j + 2U i ψi 4 (12) (cid:104)ˆb†A,iˆbA,j(cid:105) = ψA∗ ,iψ(cid:18)A,j = N(cid:19)2 eik(ri−rj)(cid:104)ˆb†A(k)ˆbA(k)(cid:105) sites − k is NEsi0tes = 3t1n + 12Un2 and we ﬁnd that the next– = n exp i2π m , (17) nearest neighbor hopping is eﬀectively cancelled. Using 3 Eq. (8), the next–nearest neighbor bond current is where m is an arbitrary integer. The condensate − − JSF = 2 n t Im exp( iπ/2) = 2nt . (13) at nonzero momentum exhibits nonuniform phase dif- AA 2 2 √ ferences between next-nearest neighbors [see Fig. 1d)]. Phase ordering directly aﬀects the next–nearest neighbor The CSF phase forms in the opposite case t < 3t . 1 2 current expectation(cid:16) value (cid:68) (cid:69)(cid:17) Non–interacting bosons can condense in a state that is an arbitrary linear combination of single particle ground states at KA and KB, leading to large degeneracy. How- JCSF = −2 Im t e−iπ/2 ˆb† ˆb ever, even weak repulsive interactions prefer a uniform AA 2 Ai Aj − − · − − density distribution on the two sublattices. To infer the = 2t n sin [ π/2 + K (r r )] = nt (.18) 2 A i j 2 low energy description, we assume that only the minima of the lowest band are occupied and approximate opera- tors according to Eq. (11) by The aforementioned “decoupling of sublattices”, Eq. (16), (cid:112) is depicted in Fig. 1d as an arbitrary phase diﬀerence be- √ ≈ 1 − tween order parameters on two sublattices. ˆbA,i (cid:112) e iKAriˆbA(KA), At the critical hopping strength t1 = 3t2, there are N /2 sites three degenerate minima present in the dispersion rela- ˆbB,i ≈ 1 e−iKBriˆbB(KB). (14) tion, and in order to deduce the proper ground state at N /2 the mean–ﬁeld level all three of them should be taken sites ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: two

text: decoupled

text: triangular

text: lattices,

text: The

label: equation

text: then

text: turns

text: into

text: and

text: we

text: expect

text: separate

text: condensation

text: of

text: bosons

text: on

text: two

text: sublattices.

text: H

text: To

text: study

text: the

text: possible

text: condensates

text: at

text: ﬁnite

text: values

text: of

text: t

text: ˆb

text: (K

text: )ˆb

text: (K

text: ˆb

text: (K

text: )ˆb

text: (K

text: A

text: A

text: A

text: A

text: B

text: B

text: B

text: B

text: and

text: t

text: let

text: us

text: focus

text: on

text: the

text: non–interacting

text: Hamiltonian.

text: The

text: dispersion

text: of

text: the

text: lowest

text: band

text: √exhibits

text: U

text: b†

text: (K

text: )ˆb

text: (K

text: b†

text: (K

text: )ˆb

text: (K

text: A

text: A

text: A

text: A

text: N

text: A

text: A

text: A

text: A

text: either

text: a

text: single

text: minimum

text: at

text: k

text: Γ

text: for

text: t

text: or

text: sites

text: degenerate

text: minima

text: at

text: the

text: two

text: inequiva√lent

text: corners

text: of

text: the

text: b

text: (K

text: )ˆb

text: (K

text: b

text: (K

text: )ˆb

text: (K

text: Brillouin

text: zone

text: KA

text: and

text: KB

text: for

text: [see

text: Fig.

text: B

text: B

text: B

text: B

text: Nsites

text: B

text: B

text: B

text: B

text: g)].

text: The

text: momenta

text: at

text: the

text: corners

text: of

text: the

text: Brillouin

text: zone

text: µ

text: ˆb

text: (K

text: )ˆb

text: (K

text: ˆb

text: (K

text: )ˆb

text: (K

text: satisfy

text: A

text: A

text: A

text: A

text: B

text: B

text: B

text: B

text: eiKA

text: bi

text: eiKB

text: bi

text: e

text: i.e.

text: it

text: describes

text: two

text: decoupled

text: sublattices

text: since

text: the

text: nearest–neighbor

text: tunneling

text: term

text: vanishes

text: for

text: all

text: i

text: At

text: these

text: high

text: symmetry

text: points,

text: the

text: Hamiltonian

text: takes

text: the

text: following

text: forms:

text: ˆbiˆbj

text: ˆbi

text: e

text: iKB

text: (ri+aj)ˆbB(KB)

text: H

text: i,j

text: i

text: (Γ)

text: σ

text: x

text: Thus

text: we

text: conclude

text: that

text: the

text: ground

text: state

text: consists

text: of

text: and

text: two

text: decoupled

text: superﬂuids.

text: The

text: same

text: observation

text: follows

text: directly

text: from

text: Eq.

text: i.

text: e.

text: at

text: the

text: mean–ﬁeld

text: level

text: the

text: H

text: ground–state

text: consists

text: of

text: two

text: separate

text: condensates

text: occu-

text: (KA,B)

text: the

text: two

text: Th√e

text: mean-ﬁeld

text: ground

text: state

text: energy

text: is

text: ordTehrepSaFrapmheatseer

text: Nco/nNdesintessaties

text: (akn)d≈thNe

text: cδorres,poρnd(ikn)g

text: ≈moNmNsδeitnetsum.

text: the

text: ﬁlling.

text: The

text: ground

text: state

text: energy

text: obtained

text: from

text: the

text: A

text: k,KA

text: B

text: k,KB

text: For

text: the

text: operators

text: ˆb

text: on

text: the

text: same

text: sublattice

text: we

text: ﬁnd

text: Gross–Pitaevskii

text: energy

text: A,i

text: from

text: Eq.

text: i,j

text: tijψi

text: i

text: ψi

text: ψA∗

text: sites

text: k

text: is

text: and

text: we

text: ﬁnd

text: that

text: the

text: next–

text: n

text: exp

text: m

text: nearest

text: neighbor

text: hopping

text: is

text: eﬀectively

text: cancelled.

text: Using

text: Eq.

text: the

text: next–nearest

text: neighbor

text: bond

text: current

text: is

text: where

text: m

text: is

text: an

text: arbitrary

text: integer.

text: The

text: condensate

text: JSF

text: n

text: t

text: Im

text: exp(

text: at

text: nonzero

text: momentum

text: exhibits

text: nonuniform

text: phase

text: dif-

text: AA

text: ferences

text: between

text: next-nearest

text: neighbors

text: [see

text: Fig.

text: Phase

text: ordering

text: directly

text: aﬀects

text: the

text: next–nearest

text: neighbor

text: The

text: CSF

text: phase

text: forms

text: in

text: the

text: opposite

text: case

text: t

text: current

text: value

text: Non–interacting

text: bosons

text: can

text: condense

text: in

text: a

text: state

text: that

text: is

text: an

text: arbitrary

text: linear

text: combination

text: of

text: single

text: particle

text: ground

text: states

text: at

text: KA

text: and

text: KB,

text: leading

text: to

text: large

text: degeneracy.

text: How-

text: JCSF

text: −2

text: Im

text: t

text: ˆb†

text: ˆb

text: ever,

text: even

text: weak

text: repulsive

text: interactions

text: prefer

text: a

text: uniform

text: AA

text: Ai

text: Aj

text: density

text: distribution

text: on

text: the

text: two

text: sublattices.

text: To

text: infer

text: the

text: n

text: sin

text: K

text: (r

text: r

text: nt

text: A

text: i

text: j

text: low

text: energy

text: description,

text: we

text: assume

text: that

text: only

text: the

text: minima

text: of

text: the

text: lowest

text: band

text: are

text: occupied

text: and

text: approximate

text: opera-

text: tors

text: according

text: to

text: Eq.

text: by

text: The

text: aforementioned

text: “decoupling

text: of

text: sublattices”,

text: Eq.

text: is

text: depicted

text: in

text: Fig.

text: as

text: an

text: arbitrary

text: phase

text: diﬀerence

text: be-

text: tween

text: order

text: parameters

text: on

text: two

text: sublattices.

text: ˆbA,i

text: e

text: iKAriˆbA(KA),

text: At

text: the

text: critical

text: hopping

text: strength

text: there

text: are

text: N

text: sites

text: three

text: degenerate

text: minima

text: present

text: in

text: the

text: dispersion

text: rela-

text: ˆbB,i

text: e−iKBriˆbB(KB).

text: tion,

text: and

text: in

text: order

text: to

text: deduce

text: the

text: proper

text: ground

text: state

text: at

text: N

text: the

text: mean–ﬁeld

text: level

text: all

text: three

text: of

text: them

text: should

text: be

text: taken

text: sites

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 7 (cid:18) Therefore, the connected correlation functions of plaque- tte currents vanish identically for separated plaquettes. U(cid:114) − − µ (cid:15) (k) (cid:33) ω± (k) = (2n 1) 2 + α This characterizes the Mott insulator phase as a state ,α 2 U U with local plaquette currents without long range current- ± (cid:15) (k) (cid:15) (k)2 current correlations. 1 + 2(2n + 1) α + α , (31) As mentioned at the beginning of the subsection, RPA U U2 is an exact description in the limit of inﬁnite coordi- ± nation number of the lattice. In the next section we where α takes values corresponding to the two non– will use bosonic DMFT to include the next–order correc- interacting bands. A detailed study of the properties of tion (i.e. a ﬁnite coordination number) and to go beyond excitations given by Eq. (31) is postponed to Sec. . Here RPA. we only note that at ﬁlling n =√ 1 the gap i√n the spec- D. DMFT − trum closes at tRPA,c = U 3 2 2 for t > 3t where 1 3 √ 1 2 the transition from the Mott insulator into the uniform Bosonic DMFT was originally introduced several years sthuepecrhﬂiuraidl soucpceurrﬂs,uwidhiislefofourntd1 f<or tR3Pt2A,tch=e tUra3n−s√2it√io2n. Tinhtoe aDgMo F[8T1–[8150]6i]n. anTahleogmy ettohtohde hwaesll–beesetnabsliuschceedssffeurlmlyioanpic- 2 3 3 two boundaries meet at the tricritical point with the line plied in the context of topological band insulators with corresponding to a direct transition between the two su- fermions [34, 38, 39, 107]. Here we use a spatially re- perﬂuids, Fig. 1b. solved version, the so–called real–space bosonic DMFT Another important feature of the Mott state are ﬁnite [108]. For completeness, we describe the method brieﬂy. (cid:81) (non–vanishing) density ﬂuctuations present at ﬁnite val- The essence of DMFT is mapping of the full lattice ues of the hopping terms t and t (note that these are problem onto a set of local problems. The next order 1 2 | (cid:105) not captured by the oversimpliﬁed state ⊗ n ). To un- correction for the self–energy in Eq. (28) is still local in i derstand how these ﬂuctuations are aﬀected by the com- space [in our case proportional to 3(t2 + 2t2)] as can be 1 2 plex hopping term (it ), we calculate local (plaquette) shown by a diagrammatic expansion [104]. To derive a 2 currents (8) between next–nearest neighbors. The expec- proper local model that goes beyond the Hamiltonian (cid:104) † (cid:105) tation value b b can be expressed in terms of Green’s (25), we perform an eﬀective integration over all oﬀ–site i j functions (cid:88) degrees of freedom and keep only terms of suitable order. We ﬁnd that the local Hamiltonian is given by a bosonic Anderson impurity model (cid:104)b†b (cid:105) = − 1 exp(iω 0+)G (iω ), (32) (cid:88) (cid:104) (cid:105) i j β n ji n n H L † † ∗ † ∗ † † i = ε aˆ aˆ + V aˆ ˆb + V aˆ ˆb + W aˆ ˆb + W aˆ ˆb where ω is Matsubara frequency. Deep in the Mott AI l l l l l i l l i l l i l l i n l=0 domain, an approximate result for G can be derived ij − ∗ − † U − − from the strong coupling expansion in hopping [104, 105]. ψAI ˆb ψAIˆb + nˆ (nˆ 1) µnˆ , (34) i i i i 2 i i i Here we consider only contributions obtained by a formal matrix inversion of Eq. (29) and by keeping terms that are second order in t . Directly from the second order (cid:104) † (cid:105) ij where index l counts Anderson orbitals and we allow result for bibj g(cid:32)iven in Ref(cid:33)s. [104, 105], we read oﬀ a for complex values of Anderson parameters Vl and Wl. general expression (cid:88) The mapping is formally described in detail in Ref. [84]. At this point it is useful to introduce hybridization func- J(2) − 3n(n + 1)(2n + 1) tions of the Anderson impurity model ij = 2Im t t t + . . . (cid:88) U ij jk ki U3 k | | | | V 2 W 2 In our case, we obtain the following perturbative result: ∆ (iω ) = (cid:88) −l + l , (cid:0) (cid:1) 11 n ε iω ε + iω l n l n l ∗ ∗ ∗ ∗ V W V W J(2) 36 − ∆ (iω ) = l− l + l l , (35) AA = t t2 2t2 . (33) 12 n ε iω ε + iω U U3 2 1 2 l l n l n ∗ ∗ On the other hand, at this order in perturbation theory and ∆ (iω ) = ∆ (iω ) , ∆ (iω ) = ∆ (iω ) . 21 n 12 n 11 n 22 n the current between nearest neighbors vanishes. The term ψAI used in Eq. (34) incorporates a correction (cid:104) (cid:105) i (cid:88) We ﬁnally note that correlations J J between with respect to the mean–ﬁeld result and it reads [84]: AA AA currents belonging to plaquettes which are separated [i.e. H − − ∗ not connected by a kinetic term in H of Eq. (2)] fac- ψiAI = tijψj ∆11(0)ψi ∆12(0)ψi . torize and are proportional to the square of Eq. (33). j ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: Therefore,

text: the

text: connected

text: correlation

text: functions

text: of

text: plaque-

text: tte

text: currents

text: vanish

text: identically

text: for

text: separated

text: plaquettes.

text: µ

text: (k)

text: ω±

text: (k)

text: α

text: This

text: characterizes

text: the

text: Mott

text: insulator

text: phase

text: as

text: a

text: state

text: ,α

text: U

text: U

text: with

text: local

text: plaquette

text: currents

text: without

text: long

text: range

text: current-

text: (k)

text: current

text: correlations.

text: α

text: α

text: As

text: mentioned

text: at

text: the

text: beginning

text: of

text: the

text: subsection,

text: RPA

text: U

text: is

text: an

text: exact

text: description

text: in

text: the

text: limit

text: of

text: inﬁnite

text: coordi-

text: nation

text: number

text: of

text: the

text: lattice.

text: In

text: the

text: next

text: section

text: we

text: where

text: α

text: takes

text: values

text: corresponding

text: to

text: the

text: two

text: non–

text: will

text: use

text: bosonic

text: DMFT

text: to

text: include

text: the

text: next–order

text: correc-

text: interacting

text: bands.

text: A

text: detailed

text: study

text: of

text: the

text: properties

text: of

text: tion

text: (i.e.

text: a

text: ﬁnite

text: coordination

text: number)

text: and

text: to

text: go

text: beyond

text: excitations

text: given

text: by

text: Eq.

text: is

text: postponed

text: to

text: Sec.

text: Here

text: RPA.

text: we

text: only

text: note

text: that

text: at

text: ﬁlling

text: n

text: the

text: gap

text: i√n

text: the

text: spec-

text: D.

text: DMFT

text: trum

text: closes

text: at

text: tRPA,c

text: U

text: for

text: t

text: where

text: the

text: transition

text: from

text: the

text: Mott

text: insulator

text: into

text: the

text: uniform

text: Bosonic

text: DMFT

text: was

text: originally

text: introduced

text: several

text: years

text: sthuepecrhﬂiuraidl

text: f<or

text: Tinhtoe

text: aDgMo

text: anTahleogmy

text: ettohtohde

text: two

text: boundaries

text: meet

text: at

text: the

text: tricritical

text: point

text: with

text: the

text: line

text: plied

text: in

text: the

text: context

text: of

text: topological

text: band

text: insulators

text: with

text: corresponding

text: to

text: a

text: direct

text: transition

text: between

text: the

text: two

text: su-

text: fermions

text: Here

text: we

text: use

text: a

text: spatially

text: re-

text: perﬂuids,

text: Fig.

text: solved

text: version,

text: the

text: so–called

text: real–space

text: bosonic

text: DMFT

text: Another

text: important

text: feature

text: of

text: the

text: Mott

text: state

text: are

text: ﬁnite

text: For

text: completeness,

text: we

text: describe

text: the

text: method

text: brieﬂy.

text: (non–vanishing)

text: density

text: ﬂuctuations

text: present

text: at

text: ﬁnite

text: val-

text: The

text: essence

text: of

text: DMFT

text: is

text: mapping

text: of

text: the

text: full

text: lattice

text: ues

text: of

text: the

text: hopping

text: terms

text: t

text: and

text: t

text: (note

text: that

text: these

text: are

text: problem

text: onto

text: a

text: set

text: of

text: local

text: problems.

text: The

text: next

text: order

text: not

text: captured

text: by

text: the

text: oversimpliﬁed

text: state

text: n

text: To

text: un-

text: correction

text: for

text: the

text: self–energy

text: in

text: Eq.

text: is

text: still

text: local

text: in

text: i

text: derstand

text: how

text: these

text: ﬂuctuations

text: are

text: aﬀected

text: by

text: the

text: com-

text: space

text: [in

text: our

text: case

text: proportional

text: to

text: as

text: can

text: be

text: plex

text: hopping

text: term

text: (it

text: we

text: calculate

text: local

text: (plaquette)

text: shown

text: by

text: a

text: diagrammatic

text: expansion

text: To

text: derive

text: a

text: currents

text: between

text: next–nearest

text: neighbors.

text: The

text: expec-

text: proper

text: local

text: model

text: that

text: goes

text: beyond

text: the

text: Hamiltonian

text: tation

text: value

text: b

text: b

text: can

text: be

text: expressed

text: in

text: terms

text: of

text: Green’s

text: we

text: perform

text: an

text: eﬀective

text: integration

text: over

text: all

text: oﬀ–site

text: i

text: j

text: functions

text: degrees

text: of

text: freedom

text: and

text: keep

text: only

text: terms

text: of

text: suitable

text: order.

text: We

text: ﬁnd

text: that

text: the

text: local

text: Hamiltonian

text: is

text: given

text: by

text: a

text: bosonic

text: Anderson

text: impurity

text: model

text: exp(iω

text: (iω

text: i

text: j

text: β

text: n

text: ji

text: n

text: n

text: H

text: L

text: i

text: ε

text: aˆ

text: aˆ

text: V

text: aˆ

text: ˆb

text: V

text: aˆ

text: ˆb

text: W

text: aˆ

text: ˆb

text: W

text: aˆ

text: ˆb

text: where

text: ω

text: is

text: Matsubara

text: frequency.

text: Deep

text: in

text: the

text: Mott

text: AI

text: l

text: l

text: l

text: l

text: l

text: i

text: l

text: l

text: i

text: l

text: l

text: i

text: l

text: l

text: i

text: n

text: domain,

text: an

text: approximate

text: result

text: for

text: G

text: can

text: be

text: derived

text: ij

text: U

text: from

text: the

text: strong

text: coupling

text: expansion

text: in

text: hopping

text: ψAI

text: ˆb

text: ψAIˆb

text: nˆ

text: (nˆ

text: µnˆ

text: i

text: i

text: i

text: i

text: i

text: i

text: i

text: Here

text: we

text: consider

text: only

text: contributions

text: obtained

text: by

text: a

text: formal

text: matrix

text: inversion

text: of

text: Eq.

text: and

text: by

text: keeping

text: terms

text: that

text: are

text: second

text: order

text: in

text: t

text: Directly

text: from

text: the

text: second

text: order

text: ij

text: where

text: index

text: l

text: counts

text: Anderson

text: orbitals

text: and

text: we

text: allow

text: result

text: for

text: bibj

text: in

text: we

text: read

text: oﬀ

text: a

text: for

text: complex

text: values

text: of

text: Anderson

text: parameters

text: Vl

text: and

text: Wl.

text: general

text: expression

text: The

text: mapping

text: is

text: formally

text: described

text: in

text: detail

text: in

text: Ref.

text: At

text: this

text: point

text: it

text: is

text: useful

text: to

text: introduce

text: hybridization

text: func-

text: tions

text: of

text: the

text: Anderson

text: impurity

text: model

text: ij

text: t

text: t

text: t

text: U

text: ij

text: jk

text: ki

text: k

text: V

text: W

text: In

text: our

text: case,

text: we

text: obtain

text: the

text: following

text: perturbative

text: result:

text: (iω

text: −l

text: l

text: n

text: ε

text: iω

text: ε

text: iω

text: l

text: n

text: l

text: n

text: l

text: V

text: W

text: V

text: W

text: (iω

text: l−

text: l

text: l

text: l

text: AA

text: t

text: n

text: ε

text: iω

text: ε

text: iω

text: U

text: l

text: l

text: n

text: l

text: n

text: On

text: the

text: other

text: hand,

text: at

text: this

text: order

text: in

text: perturbation

text: theory

text: and

text: (iω

text: (iω

text: (iω

text: (iω

text: n

text: n

text: n

text: n

text: the

text: current

text: between

text: nearest

text: neighbors

text: vanishes.

text: The

text: term

text: ψAI

text: used

text: in

text: Eq.

text: incorporates

text: a

text: correction

text: i

text: We

text: ﬁnally

text: note

text: that

text: correlations

text: J

text: J

text: between

text: with

text: respect

text: to

text: the

text: mean–ﬁeld

text: result

text: and

text: it

text: reads

text: AA

text: AA

text: currents

text: belonging

text: to

text: plaquettes

text: which

text: are

text: separated

text: [i.e.

text: H

text: not

text: connected

text: by

text: a

text: kinetic

text: term

text: in

text: H

text: of

text: Eq.

text: fac-

text: ψiAI

text: tijψj

text: torize

text: and

text: are

text: proportional

text: to

text: the

text: square

text: of

text: Eq.

text: j

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 9 0.1 a) 0.12 b) 0.08 SF 0.14 0.14 0.05 0.07 0.1 0.12 0.12 U 0.06 /A 0 0.1 0.08 0.1 A 0.05 J t /U = 0.04 -0.05 tt111//UU == 00..1102 t/U1 00..0068 0.06 00..0068 00..0034 -0.1 t1/U = 0.14 CSF 0.04 0.04 0.04 0.02 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.02 0.02 0.02 0.01 t /U 2 0 0 0 0 0 0.04 0.08 0 0.04 0.08 FIG. 5. (Color online) The J current vs. t for n = 1 and c) 0.7 d) 0.3 AA 2 0.14 0.14 several values of t . Deep in SF (upper left) the current is 1 0.6 0.25 positive and exhibits linear increase with t . In CSF (bottom 0.12 0.12 2 right) the current is negative, strongly dependent on t and 0.5 | | 2 0.1 0.1 0.2 only weakly aﬀected by t . The absolute value J is much 1 AA 0.4 weaker in MI (intermediate regions). U 0.08 0.08 0.15 t/1 0.06 0.3 0.06 √ 0.1 0.04 0.2 0.04 change occurs for t1 = 2t2, Fig. 4. At stronger values of 0.02 0.1 0.02 0.05 t and t , there are more features showing up, Fig. 5. In 1 2 0 0 0 0 agreement with Eqs. (13) and (18), J is positive in the AA 0 0.04 0.08 0 0.04 0.08 SF, and negative in the CSF. By increasing t and keep- 2 t /U t /U 2 2 ing t small enough (for example t /U = 0.04 in Fig. 5) 1 1 we reach the point of the second order PMI –CSF tran- FIG. 6. (Color online) Comparison of DMFT (a) and c)) and sition. The aforementioned reentrant phase transition is ED results (b) and d)). Absolute value of the current on the | | marked by two second–order phase transitions from the bond between two next–nearest neighbors J /U is shown AA SF into PMI and from the PMI into the CSF, for ex- in a) and b). In c) and d) we plot local density ﬂuctuations (cid:104) (cid:105) − (cid:104) (cid:105) ample for t1/U = 0.10. It is interesting to note the non- nˆ2i nˆi 2. The inset in a) gives th√e sign of JAA: In√the monotonic behavior - the absolute value of JAA initially superﬂuid, the sign changes for t1 = 3t2 (solid line), while exhibits a linear increase with t , but as we approach the deep in the Mott domain the boundary is given by t1 = 2t2 2 (dashed line). DMFT data shown in these plots are for the Mott domain it decays due to a reduced value of the or- ﬁxed value of chemical potential µ/U = 0.4, while ED re- der parameter. At strong enough t and t , we expect the 1 2 sults are at ﬁxed ﬁlling n = 1. However, the main features intermediate Mott domain to vanish and the ﬁrst order discussed in the text are clearly visible. phase transition described in section to set in. E. Exact diagonalization As shown in Sec. , bond current expectation values dis- In this section we use the ALPS implementation [110] tinguish the chiral superﬂuid from the uniform superﬂuid of the Lanczos algorithm [111] in order to study the phase. The nearest neighbor current JAB vanishes iden- ground state of the interacting model in Eq. (5) at unit tically at n = 1. The next-nearest neighbor bond current × ﬁlling n = 1. We consider a lattice of 3 3 unit cells, im- JAA as a function of t1 and t2 is consistent with the re- plying N = 18 and N = 18 particles. The truncated sult from strong-coupling perturbation theory [Eq. (33)]. sites √ boson Hilbert space contains states for which the(cid:104)nu(cid:105)m≤ber The next-nearest neighbor current JAA changes sign at expectation val(cid:80)ue at any site is bounded above ni 2. t1 = t2 3, and JBB has analogous behavior [their com- The Hilbert subspace with this constraint has dimension mon absolute value is plotted in Figure 6b)]. This is the 44152809. With periodic boundary conditions, total mo- exact phase boundary found previously in the weakly in- mentum Q = N k is a good quantum number and teracting regime and with DMFT for arbitrarily strong i=1 i the dimension of the Hilbert space for each momentum interactions. We thus conﬁrm the existence of the PMI sector is reduced by a factor of 9. The Brillouin zone con- state with nonzero triangular plaquette currents at order × tains 3 3 points and includes the inequivalent points Γ t21t2/U3 but vanishing nearest-neighbor currents. and K , K , as shown in Figure 7. To understand the momentum structure of the ground A B Since total particle number is conserved, the sponta- state, we consider the momen(cid:88)tum distributions, neous breaking of the U(1) symmetry is not observable in the ground state. We rather identify the Mott insula- ≡ (cid:104) † (cid:105) · (cid:104) † (cid:105) tor phase as the region of the(cid:104)(t1(cid:105)/−U,(cid:104)t2/(cid:105)U) plane where na(k) ˆba(k)ˆba(k) = eik rj ˆba0ˆbaj , (38) number ﬂuctuations at a site n2 n 2 are small [see j i i Figure 6d)]. ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

font: default

text: a)

text: b)

text: SF

text: U

text: /A

text: A

text: J

text: t

text: /U

text: CSF

text: t

text: /U

text: FIG.

text: (Color

text: online)

text: The

text: J

text: current

text: vs.

text: t

text: for

text: n

text: and

text: c)

text: d)

text: AA

text: several

text: values

text: of

text: t

text: Deep

text: in

text: SF

text: (upper

text: left)

text: the

text: current

text: is

text: positive

text: and

text: exhibits

text: linear

text: increase

text: with

text: t

text: In

text: CSF

text: (bottom

text: right)

text: the

text: current

text: is

text: negative,

text: strongly

text: dependent

text: on

text: t

text: and

text: only

text: weakly

text: aﬀected

text: by

text: t

text: The

text: absolute

text: value

text: J

text: is

text: much

text: AA

text: weaker

text: in

text: MI

text: (intermediate

text: regions).

text: U

text: change

text: occurs

text: for

text: Fig.

text: At

text: stronger

text: values

text: of

text: t

text: and

text: t

text: there

text: are

text: more

text: features

text: showing

text: up,

text: Fig.

text: In

text: agreement

text: with

text: Eqs.

text: and

text: J

text: is

text: positive

text: in

text: the

text: AA

text: SF,

text: and

text: negative

text: in

text: the

text: CSF.

text: By

text: increasing

text: t

text: and

text: keep-

text: t

text: /U

text: t

text: /U

text: ing

text: t

text: small

text: enough

text: (for

text: example

text: t

text: /U

text: in

text: Fig.

text: we

text: reach

text: the

text: point

text: of

text: the

text: second

text: order

text: PMI

text: –CSF

text: tran-

text: FIG.

text: (Color

text: online)

text: Comparison

text: of

text: DMFT

text: (a)

text: and

text: c))

text: and

text: sition.

text: The

text: aforementioned

text: reentrant

text: phase

text: transition

text: is

text: ED

text: results

text: (b)

text: and

text: d)).

text: Absolute

text: value

text: of

text: the

text: current

text: on

text: the

text: marked

text: by

text: two

text: second–order

text: phase

text: transitions

text: from

text: the

text: bond

text: between

text: two

text: next–nearest

text: neighbors

text: J

text: /U

text: is

text: shown

text: AA

text: SF

text: into

text: PMI

text: and

text: from

text: the

text: PMI

text: into

text: the

text: CSF,

text: for

text: ex-

text: in

text: a)

text: and

text: b).

text: In

text: c)

text: and

text: d)

text: we

text: plot

text: local

text: density

text: ﬂuctuations

text: ample

text: for

text: It

text: is

text: interesting

text: to

text: note

text: the

text: non-

text: nˆi

text: The

text: inset

text: in

text: a)

text: gives

text: th√e

text: sign

text: of

text: JAA:

text: In√the

text: monotonic

text: behavior

text: the

text: absolute

text: value

text: of

text: JAA

text: initially

text: superﬂuid,

text: the

text: sign

text: changes

text: for

text: (solid

text: line),

text: while

text: exhibits

text: a

text: linear

text: increase

text: with

text: t

text: but

text: as

text: we

text: approach

text: the

text: deep

text: in

text: the

text: Mott

text: domain

text: the

text: boundary

text: is

text: given

text: by

text: (dashed

text: line).

text: DMFT

text: data

text: shown

text: in

text: these

text: plots

text: are

text: for

text: the

text: Mott

text: domain

text: it

text: decays

text: due

text: to

text: a

text: reduced

text: value

text: of

text: the

text: or-

text: ﬁxed

text: value

text: of

text: chemical

text: potential

text: µ/U

text: while

text: ED

text: re-

text: der

text: parameter.

text: At

text: strong

text: enough

text: t

text: and

text: t

text: we

text: expect

text: the

text: sults

text: are

text: at

text: ﬁxed

text: ﬁlling

text: n

text: However,

text: the

text: main

text: features

text: intermediate

text: Mott

text: domain

text: to

text: vanish

text: and

text: the

text: ﬁrst

text: order

text: discussed

text: in

text: the

text: text

text: are

text: clearly

text: visible.

text: phase

text: transition

text: described

text: in

text: section

text: to

text: set

text: in.

text: E.

text: Exact

text: diagonalization

text: As

text: shown

text: in

text: Sec.

text: bond

text: current

text: expectation

text: values

text: dis-

text: In

text: this

text: section

text: we

text: use

text: the

text: ALPS

text: implementation

text: tinguish

text: the

text: chiral

text: superﬂuid

text: from

text: the

text: uniform

text: superﬂuid

text: of

text: the

text: Lanczos

text: algorithm

text: in

text: order

text: to

text: study

text: the

text: phase.

text: The

text: nearest

text: neighbor

text: current

text: JAB

text: vanishes

text: iden-

text: ground

text: state

text: of

text: the

text: interacting

text: model

text: in

text: Eq.

text: at

text: unit

text: tically

text: at

text: n

text: The

text: next-nearest

text: neighbor

text: bond

text: current

text: ﬁlling

text: n

text: We

text: consider

text: a

text: lattice

text: of

text: unit

text: cells,

text: im-

text: JAA

text: as

text: a

text: function

text: of

text: and

text: is

text: consistent

text: with

text: the

text: re-

text: plying

text: N

text: and

text: N

text: particles.

text: The

text: truncated

text: sult

text: from

text: strong-coupling

text: perturbation

text: theory

text: [Eq.

text: sites

text: boson

text: Hilbert

text: space

text: contains

text: states

text: for

text: which

text: The

text: next-nearest

text: neighbor

text: current

text: JAA

text: changes

text: sign

text: at

text: expectation

text: at

text: any

text: site

text: is

text: bounded

text: above

text: ni

text: and

text: JBB

text: has

text: analogous

text: behavior

text: [their

text: com-

text: The

text: Hilbert

text: subspace

text: with

text: this

text: constraint

text: has

text: dimension

text: mon

text: absolute

text: value

text: is

text: plotted

text: in

text: Figure

text: This

text: is

text: the

text: With

text: periodic

text: boundary

text: conditions,

text: total

text: mo-

text: exact

text: phase

text: boundary

text: found

text: previously

text: in

text: the

text: weakly

text: in-

text: mentum

text: Q

text: N

text: k

text: is

text: a

text: good

text: quantum

text: number

text: and

text: teracting

text: regime

text: and

text: with

text: DMFT

text: for

text: arbitrarily

text: strong

text: i

text: the

text: dimension

text: of

text: the

text: Hilbert

text: space

text: for

text: each

text: momentum

text: interactions.

text: We

text: thus

text: conﬁrm

text: the

text: existence

text: of

text: the

text: PMI

text: sector

text: is

text: reduced

text: by

text: a

text: factor

text: of

text: The

text: Brillouin

text: zone

text: con-

text: state

text: with

text: nonzero

text: triangular

text: plaquette

text: currents

text: at

text: order

text: tains

text: points

text: and

text: includes

text: the

text: inequivalent

text: points

text: Γ

text: but

text: vanishing

text: nearest-neighbor

text: currents.

text: and

text: K

text: K

text: as

text: shown

text: in

text: Figure

text: To

text: understand

text: the

text: momentum

text: structure

text: of

text: the

text: ground

text: A

text: B

text: Since

text: total

text: particle

text: number

text: is

text: conserved,

text: the

text: sponta-

text: state,

text: we

text: consider

text: the

text: distributions,

text: neous

text: breaking

text: of

text: the

text: symmetry

text: is

text: not

text: observable

text: in

text: the

text: ground

text: state.

text: We

text: rather

text: identify

text: the

text: Mott

text: insula-

text: tor

text: phase

text: as

text: the

text: region

text: of

text: plane

text: where

text: na(k)

text: ˆba(k)ˆba(k)

text: eik

text: rj

text: number

text: ﬂuctuations

text: at

text: a

text: site

text: n

text: are

text: small

text: [see

text: j

text: i

text: i

text: Figure

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 4 × − FIG. 4. Outer: Evolutions of the NLOPs found in diﬀerent length pipes at E = 1.6 10 4. All four optimals initially have 0 indistinguishable evolutions, before they begin to separate. For the two longest domains they remain inseparable throughout the evolution period. Inner: The axial distribution of the initial energy of the same NLOPs. The central structure of the diﬀering optimals closely match, diverging only as the ends of the periodic domain are reached. FIG. 5. Evolution of optimals with diﬀering T. The two blue (dark thin )lines have very short optimsation times (T = 12.5 D/U ≥ and 15.5 D/U). These two optimals evolve in a notably diﬀerent manner to all the other optimals (T 16 D/U) being considered. The optimal corresponding to T = T is shown in (thick) red, while the largest optimisation time considered lin (T = 100D/U) is shown in cyan (only the ﬁrst 40 D/U is plotted). The two dashed lines correspond to T = 15.5 D/U (blue/dark) and T = 16 D/U (green/light) which bracket the abrupt change in evolution of their respective optimals. (cid:38) (cid:39) T 16D/U the optimals all evolved in similar manners, reaching a peak energy level at T 20D/U before decaying away. Smaller values of T give an optimal which undergoes an accelerated evolution. The eventual maximum energy levels obtained (were the perturbation allowed to evolve indeﬁnitely) are lower than before, and the transition between these two types of evolution is abrupt – the optimals for T = 15.5D/U and T = 16D/U are indicated by dashed lines in Fig. 5. Unless short times are taken, the optimal observed is relatively insensitive to the value of T chosen. Previous work18,22 conjectured, and provided evidence that, if large optimisation times are used then the nonlinear transient growth algorithm can be used to identify both the minimum amplitude of disturbance required to trigger turbulence, and the minimum seed that this equates to. Due to the computationally demanding nature of the computation even in short domains, in this work we have considered intermediate optimisation times. Nonetheless, it appears clear that this is suﬃcient to observe the form of the minimal seed. 1100 1 1000 0.8 0.6 900 S d 0.4 800 0.2 0 G 700 3 3.5 4 4.5 5 L 600 500 400 300 2 3 4 5 6 7 8 9 10 L (D) FIG. 6. Growth against length of pipe L (in D) for the streamwise independent optimal, QLOP (green), the nonlinear optimal, NLOP (red) and the nonlinear optimal with shift-and-reﬂect symmetry enforced with in the domain (blue). The switch in (cid:39) optimal type can clearly be seen at L 3.5 D with the shift-and-reﬂect optimal being the global optimal for shorter domains than this. The inset demonstrates that the switchover is not a bifurcation but merely a crossing over of distinct maximums as the energy in the symmetry-breaking part of the large L optimal does not vanish at the switchover length. All results are for × − ﬁxed E = 0.8 10 4. 0 ##LTFigure## ##LTLine##

label: caption

text: FIG.

text: Outer:

text: Evolutions

text: of

text: the

text: NLOPs

text: found

text: in

text: diﬀerent

text: length

text: pipes

text: at

text: E

text: All

text: four

text: optimals

text: initially

text: have

text: indistinguishable

text: evolutions,

text: before

text: they

text: begin

text: to

text: separate.

text: For

text: the

text: two

text: longest

text: domains

text: they

text: remain

text: inseparable

text: throughout

text: the

text: evolution

text: period.

text: Inner:

text: The

text: axial

text: distribution

text: of

text: the

text: initial

text: energy

text: of

text: the

text: same

text: NLOPs.

text: The

text: central

text: structure

text: of

text: the

text: diﬀering

text: optimals

text: closely

text: match,

text: diverging

text: only

text: as

text: the

text: ends

text: of

text: the

text: periodic

text: domain

text: are

text: reached.

text: FIG.

text: Evolution

text: of

text: optimals

text: with

text: diﬀering

text: T.

text: The

text: two

text: blue

text: (dark

text: thin

text: )lines

text: have

text: very

text: short

text: optimsation

text: times

text: (T

text: D/U

text: and

text: D/U).

text: These

text: two

text: optimals

text: evolve

text: in

text: a

text: notably

text: diﬀerent

text: manner

text: to

text: all

text: the

text: other

text: optimals

text: (T

text: D/U)

text: being

text: considered.

text: The

text: optimal

text: corresponding

text: to

text: T

text: T

text: is

text: shown

text: in

text: (thick)

text: red,

text: while

text: the

text: largest

text: optimisation

text: time

text: considered

text: lin

text: (T

text: is

text: shown

text: in

text: cyan

text: (only

text: the

text: ﬁrst

text: D/U

text: is

text: plotted).

text: The

text: two

text: dashed

text: lines

text: correspond

text: to

text: T

text: D/U

text: (blue/dark)

text: and

text: T

text: D/U

text: (green/light)

text: which

text: bracket

text: the

text: abrupt

text: change

text: in

text: evolution

text: of

text: their

text: respective

text: optimals.

text: T

text: the

text: optimals

text: all

text: evolved

text: in

text: similar

text: manners,

text: reaching

text: a

text: peak

text: energy

text: level

text: at

text: T

text: before

text: decaying

text: away.

text: Smaller

text: values

text: of

text: T

text: give

text: an

text: optimal

text: which

text: undergoes

text: an

text: accelerated

text: evolution.

text: The

text: eventual

text: maximum

text: energy

text: levels

text: obtained

text: (were

text: the

text: perturbation

text: allowed

text: to

text: evolve

text: indeﬁnitely)

text: are

text: lower

text: than

text: before,

text: and

text: the

text: transition

text: between

text: these

text: two

text: types

text: of

text: evolution

text: is

text: abrupt

text: the

text: optimals

text: for

text: T

text: and

text: T

text: are

text: indicated

text: by

text: dashed

text: lines

text: in

text: Fig.

text: Unless

text: short

text: times

text: are

text: taken,

text: the

text: optimal

text: observed

text: is

text: relatively

text: insensitive

text: to

text: the

text: value

text: of

text: T

text: chosen.

text: Previous

text: conjectured,

text: and

text: provided

text: evidence

text: that,

text: if

text: large

text: optimisation

text: times

text: are

text: used

text: then

text: the

text: nonlinear

text: transient

text: growth

text: algorithm

text: can

text: be

text: used

text: to

text: identify

text: both

text: the

text: minimum

text: amplitude

text: of

text: disturbance

text: required

text: to

text: trigger

text: turbulence,

text: and

text: the

text: minimum

text: seed

text: that

text: this

text: equates

text: to.

text: Due

text: to

text: the

text: computationally

text: demanding

text: nature

text: of

text: the

text: computation

text: even

text: in

text: short

text: domains,

text: in

text: this

text: work

text: we

text: have

text: considered

text: intermediate

text: optimisation

text: times.

text: Nonetheless,

text: it

text: appears

text: clear

text: that

text: this

text: is

text: suﬃcient

text: to

text: observe

text: the

text: form

text: of

text: the

text: minimal

text: seed.

text: S

text: d

text: G

text: L

text: L

text: (D)

text: FIG.

text: Growth

text: against

text: length

text: of

text: pipe

text: L

text: (in

text: D)

text: for

text: the

text: streamwise

text: independent

text: optimal,

text: QLOP

text: (green),

text: the

text: nonlinear

text: optimal,

text: NLOP

text: (red)

text: and

text: the

text: nonlinear

text: optimal

text: with

text: shift-and-reﬂect

text: symmetry

text: enforced

text: with

text: in

text: the

text: domain

text: (blue).

text: The

text: switch

text: in

text: optimal

text: type

text: can

text: clearly

text: be

text: seen

text: at

text: L

text: D

text: with

text: the

text: shift-and-reﬂect

text: optimal

text: being

text: the

text: global

text: optimal

text: for

text: shorter

text: domains

text: than

text: this.

text: The

text: inset

text: demonstrates

text: that

text: the

text: switchover

text: is

text: not

text: a

text: bifurcation

text: but

text: merely

text: a

text: crossing

text: over

text: of

text: distinct

text: maximums

text: as

text: the

text: energy

text: in

text: the

text: symmetry-breaking

text: part

text: of

text: the

text: large

text: L

text: optimal

text: does

text: not

text: vanish

text: at

text: the

text: switchover

text: length.

text: All

text: results

text: are

text: for

text: ﬁxed

text: E

text: ##LTFigure##

text: ##LTLine##


text: Mobile Device Identiﬁcation via Sensor Fingerprinting Hristo Bojinov Dan Boneh Yan Michalevsky Stanford University Stanford University Stanford University Gabi Nakibly National Research & Simulation Center, Rafael Ltd. Abstract on the device. Later the user resets the device to its fac- We demonstrate how the multitude of sensors on a smart- tory settings thereby deleting the app and its stored iden- phone can be used to construct a reliable hardware ﬁn- tiﬁer. The user then re-installs the app and connects to gerprint of the phone. Such a ﬁngerprint can be used the cloud service. At this point the service cannot tell to de-anonymize mobile devices as they connect to web whether it has already seen the device before. This sim- sites, and as a second factor in identifying legitimate ple trick may allow a misbehaving user whose account users to a remote server. We present two implementa- was blocked to reconnect to the service using a different tions: one based on analyzing the frequency response identity. of the speakerphone-microphone system, and another More generally, online device identiﬁcation is a topic based on analyzing device-speciﬁc accelerometer cali- of much interest to advertising networks and organiza- bration errors. Our accelerometer-based ﬁngerprint is es- tions providing security services. The need to identify pecially interesting because the accelerometer is accessi- remote peers is always pitted against concerns that iden- ble via JavaScript running in a mobile web browser with- tifying information may be misused. Rapidly evolving out requesting any permissions or notifying the user. We mobile technologies pose new challenges to preserving present the results of the most extensive sensor ﬁnger- user privacy and one of our goals in this paper is to ex- printing experiment done to date, which measured sensor plore these challenges, and inform the design of future properties from over 10,000 mobile devices. We show mobile device platforms. that the entropy from sensor ﬁngerprinting is sufﬁcient to To obtain a robust identiﬁer for mobile devices many uniquely identify a device among thousands of devices, app developers have turned to a hardware ID that sur- with low probability of collision. vives a device reset to factory settings. A recent study shows that 8% of Android apps use the International 1 Introduction Mobile Equipment Identity (IMEI) as a hardware device ID [19]. This type of practice is frowned upon to the Many Internet services need reliable identiﬁers to point that Apple disallows apps who read the iOS Uni- identify repeat visitors. The simplest identiﬁer, a Web versal Device ID (UDID) on their app store [25]. cookie, works well, but is unreliable in case users clear Our contribution. We show that the multitude of sen- cookies, block 3rd party cookies, or use private browsing sors on a modern smartphone can be used to build a ro- mode. This lead to the development of stronger identi- bust device ID, or ﬁngerprint, that is independent of the ﬁers such as supercookies. The Panopticlick project [18] software state and survives a hard reset. Our results show showed that desktop browsers are sufﬁciently different a unique device ﬁngerprint can be computed without ac- to be identiﬁed. However, the project noted that mobile cessing traditional hardware identiﬁers such as the IMEI browsers, especially on iOS, are too similar for this ap- or UDID. Consequently, simply disallowing app access proach to work. to the device UDID is an ineffective privacy policy. The need for robust identiﬁers is even stronger on mo- We experiment with ﬁngerprinting using two sensors: bile devices. First, as above, Web sites wish to iden- • tify repeat visitors. Second, cloud-based services who The speakerphone-microphone system: the ﬁn- develop mobile applications often need a robust phone gerprinting system uses the speakers to emit a identiﬁer. Consider the following scenario: a user in- sequence of sounds at different frequencies and stalls a cloud-based app and the app installs an identiﬁer records the resulting signals using the microphone.

text: Mobile

label: title

text: Device

text: Identiﬁcation

text: via

text: Sensor

text: Fingerprinting

text: Hristo

label: author

text: Bojinov

text: Dan

text: Boneh

text: Yan

text: Michalevsky

text: Stanford

text: University

text: Stanford

text: University

text: Stanford

text: University

text: Gabi

text: Nakibly

text: National

text: Research

text: Simulation

text: Center,

text: Rafael

text: Ltd.

text: Abstract

text: on

text: the

text: device.

text: Later

text: the

text: user

text: resets

text: the

text: device

text: to

text: its

text: fac-

text: We

label: abstract

text: demonstrate

text: how

text: the

text: multitude

text: of

text: sensors

text: on

text: a

text: smart-

text: tory

text: settings

text: thereby

text: deleting

text: the

text: app

text: and

text: its

text: stored

text: iden-

text: phone

text: can

text: be

text: used

text: to

text: construct

text: a

text: reliable

text: hardware

text: ﬁn-

text: tiﬁer.

text: The

text: user

text: then

text: re-installs

text: the

text: app

text: and

text: connects

text: to

text: gerprint

text: of

text: the

text: phone.

text: Such

text: a

text: ﬁngerprint

text: can

text: be

text: used

text: the

text: cloud

text: service.

text: At

text: this

text: point

text: the

text: service

text: cannot

text: tell

text: to

text: de-anonymize

text: mobile

text: devices

text: as

text: they

text: connect

text: to

text: web

text: whether

text: it

text: has

text: already

text: seen

text: the

text: device

text: before.

text: This

text: sim-

text: sites,

text: and

text: as

text: a

text: second

text: factor

text: in

text: identifying

text: legitimate

text: ple

text: trick

text: may

text: allow

text: a

text: misbehaving

text: user

text: whose

text: account

text: users

text: to

text: a

text: remote

text: server.

text: We

text: present

text: two

text: implementa-

text: was

text: blocked

text: to

text: reconnect

text: to

text: the

text: service

text: using

text: a

text: different

text: tions:

text: one

text: based

text: on

text: analyzing

text: the

text: frequency

text: response

text: identity.

text: of

text: the

text: speakerphone-microphone

text: system,

text: and

text: another

text: More

text: generally,

text: online

text: device

text: identiﬁcation

text: is

text: a

text: topic

text: based

text: on

text: analyzing

text: device-speciﬁc

text: accelerometer

text: cali-

text: of

text: much

text: interest

text: to

text: advertising

text: networks

text: and

text: organiza-

text: bration

text: errors.

text: Our

text: accelerometer-based

text: ﬁngerprint

text: is

text: es-

text: tions

text: providing

text: security

text: services.

text: The

text: need

text: to

text: identify

text: pecially

text: interesting

text: because

text: the

text: accelerometer

text: is

text: accessi-

text: remote

text: peers

text: is

text: always

text: pitted

text: against

text: concerns

text: that

text: iden-

text: ble

text: via

text: JavaScript

text: running

text: in

text: a

text: mobile

text: web

text: browser

text: with-

text: tifying

text: information

text: may

text: be

text: misused.

text: Rapidly

text: evolving

text: out

text: requesting

text: any

text: permissions

text: or

text: notifying

text: the

text: user.

text: We

text: mobile

text: technologies

text: pose

text: new

text: challenges

text: to

text: preserving

text: present

text: the

text: results

text: of

text: the

text: most

text: extensive

text: sensor

text: ﬁnger-

text: user

text: privacy

text: and

text: one

text: of

text: our

text: goals

text: in

text: this

text: paper

text: is

text: to

text: ex-

text: printing

text: experiment

text: done

text: to

text: date,

text: which

text: measured

text: sensor

text: plore

text: these

text: challenges,

text: and

text: inform

text: the

text: design

text: of

text: future

text: properties

text: from

text: over

text: mobile

text: devices.

text: We

text: show

text: mobile

text: device

text: platforms.

text: that

text: the

text: entropy

text: from

text: sensor

text: ﬁngerprinting

text: is

text: sufﬁcient

text: to

text: To

text: obtain

text: a

text: robust

text: identiﬁer

text: for

text: mobile

text: devices

text: many

text: uniquely

text: identify

text: a

text: device

text: among

text: thousands

text: of

text: devices,

text: app

text: developers

text: have

text: turned

text: to

text: a

text: hardware

text: ID

text: that

text: sur-

text: with

text: low

text: probability

text: of

text: collision.

text: vives

text: a

text: device

text: reset

text: to

text: factory

text: settings.

text: A

text: recent

text: study

text: shows

text: that

text: of

text: Android

text: apps

text: use

text: the

text: International

text: Introduction

text: Mobile

text: Equipment

text: Identity

text: (IMEI)

text: as

text: a

text: hardware

text: device

text: ID

text: This

text: type

text: of

text: practice

text: is

text: frowned

text: upon

text: to

text: the

text: Many

text: Internet

text: services

text: need

text: reliable

text: identiﬁers

text: to

text: point

text: that

text: Apple

text: disallows

text: apps

text: who

text: read

text: the

text: iOS

text: Uni-

text: identify

text: repeat

text: visitors.

text: The

text: simplest

text: identiﬁer,

text: a

text: Web

text: versal

text: Device

text: ID

text: (UDID)

text: on

text: their

text: app

text: store

text: cookie,

text: works

text: well,

text: but

text: is

text: unreliable

text: in

text: case

text: users

text: clear

text: Our

text: contribution.

text: We

text: show

text: that

text: the

text: multitude

text: of

text: sen-

text: cookies,

text: block

text: party

text: cookies,

text: or

text: use

text: private

text: browsing

text: sors

text: on

text: a

text: modern

text: smartphone

text: can

text: be

text: used

text: to

text: build

text: a

text: ro-

text: mode.

text: This

text: lead

text: to

text: the

text: development

text: of

text: stronger

text: identi-

text: bust

text: device

text: ID,

text: or

text: ﬁngerprint,

text: that

text: is

text: independent

text: of

text: the

text: ﬁers

text: such

text: as

text: supercookies.

text: The

text: Panopticlick

text: project

text: software

text: state

text: and

text: survives

text: a

text: hard

text: reset.

text: Our

text: results

text: show

text: showed

text: that

text: desktop

text: browsers

text: are

text: sufﬁciently

text: different

text: a

text: unique

text: device

text: ﬁngerprint

text: can

text: be

text: computed

text: without

text: ac-

text: to

text: be

text: identiﬁed.

text: However,

text: the

text: project

text: noted

text: that

text: mobile

text: cessing

text: traditional

text: hardware

text: identiﬁers

text: such

text: as

text: the

text: IMEI

text: browsers,

text: especially

text: on

text: iOS,

text: are

text: too

text: similar

text: for

text: this

text: ap-

text: or

text: UDID.

text: Consequently,

text: simply

text: disallowing

text: app

text: access

text: proach

text: to

text: work.

text: to

text: the

text: device

text: UDID

text: is

text: an

text: ineffective

text: privacy

text: policy.

text: The

text: need

text: for

text: robust

text: identiﬁers

text: is

text: even

text: stronger

text: on

text: mo-

text: We

text: experiment

text: with

text: ﬁngerprinting

text: using

text: two

text: sensors:

text: bile

text: devices.

text: First,

text: as

text: above,

text: Web

text: sites

text: wish

text: to

text: iden-

text: tify

text: repeat

text: visitors.

text: Second,

text: cloud-based

text: services

text: who

text: The

text: speakerphone-microphone

text: system:

text: the

text: ﬁn-

text: develop

text: mobile

text: applications

text: often

text: need

text: a

text: robust

text: phone

text: gerprinting

text: system

text: uses

text: the

text: speakers

text: to

text: emit

text: a

text: identiﬁer.

text: Consider

text: the

text: following

text: scenario:

text: a

text: user

text: in-

text: sequence

text: of

text: sounds

text: at

text: different

text: frequencies

text: and

text: stalls

text: a

text: cloud-based

text: app

text: and

text: the

text: app

text: installs

text: an

text: identiﬁer

text: records

text: the

text: resulting

text: signals

text: using

text: the

text: microphone.


text: it would be, for example, to record the exact locations of the user’s taps on the keyboard display. Averaging the tap locations for each key and comparing it against the actual key’s location at the keyboard display may allow one to calculate the misalignment. Nonetheless, we ex- pect this method to be highly dependent on the user as much as the touch screen misalignment. Camera: There are a few works that deal with cam- era identiﬁcation using the pixels’ bias. The output gain of each pixel is a linear function of the actual intensity of light hitting that pixel. This linear bias is commonly called pattern noise; [28] proposes a method to determine a camera’s reference pattern noise using a 300 pictures taken by that camera. This serves as a unique ﬁngerprint for the camera. It is shown that this enables to associate with good probability a new picture with the camera that took it. The study was done using 9 cameras. How- ever, no effort was done to assess the expected number of cameras that can be distinguished using this method, and what is more, most of the cameras differ in either model or manufacturer which tends to make identiﬁca- tion easier (some evidence is presented however that the results can carry over to identical cameras as well). 14

text: it

text: would

text: be,

text: for

text: example,

text: to

text: record

text: the

text: exact

text: locations

text: of

text: the

text: user’s

text: taps

text: on

text: the

text: keyboard

text: display.

text: Averaging

text: the

text: tap

text: locations

text: for

text: each

text: key

text: and

text: comparing

text: it

text: against

text: the

text: actual

text: key’s

text: location

text: at

text: the

text: keyboard

text: display

text: may

text: allow

text: one

text: to

text: calculate

text: the

text: misalignment.

text: Nonetheless,

text: we

text: ex-

text: pect

text: this

text: method

text: to

text: be

text: highly

text: dependent

text: on

text: the

text: user

text: as

text: much

text: as

text: the

text: touch

text: screen

text: misalignment.

text: Camera:

text: There

text: are

text: a

text: few

text: works

text: that

text: deal

text: with

text: cam-

text: era

text: identiﬁcation

text: using

text: the

text: pixels’

text: bias.

text: The

text: output

text: gain

text: of

text: each

text: pixel

text: is

text: a

text: linear

text: function

text: of

text: the

text: actual

text: intensity

text: of

text: light

text: hitting

text: that

text: pixel.

text: This

text: linear

text: bias

text: is

text: commonly

text: called

text: pattern

text: noise;

text: proposes

text: a

text: method

text: to

text: determine

text: a

text: camera’s

text: reference

text: pattern

text: noise

text: using

text: a

text: pictures

text: taken

text: by

text: that

text: camera.

text: This

text: serves

text: as

text: a

text: unique

text: ﬁngerprint

text: for

text: the

text: camera.

text: It

text: is

text: shown

text: that

text: this

text: enables

text: to

text: associate

text: with

text: good

text: probability

text: a

text: new

text: picture

text: with

text: the

text: camera

text: that

text: took

text: it.

text: The

text: study

text: was

text: done

text: using

text: cameras.

text: How-

text: ever,

text: no

text: effort

text: was

text: done

text: to

text: assess

text: the

text: expected

text: number

text: of

text: cameras

text: that

text: can

text: be

text: distinguished

text: using

text: this

text: method,

text: and

text: what

text: is

text: more,

text: most

text: of

text: the

text: cameras

text: differ

text: in

text: either

text: model

text: or

text: manufacturer

text: which

text: tends

text: to

text: make

text: identiﬁca-

text: tion

text: easier

text: (some

text: evidence

text: is

text: presented

text: however

text: that

text: the

text: results

text: can

text: carry

text: over

text: to

text: identical

text: cameras

text: as

text: well).