Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model

Iemini, Fernando; Maciel, Thiago O.; Vianna, Reinaldo O.

doi:10.1103/physrevb.92.075423

Cited by 56 publications

(45 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Quantum information measures have been known for some time to show signatures at continuous and discrete phase transitions, both at T = 0 and finite temperature [61][62][63][64][65][66][67][68][69][70][71][72][73][74] including the case of spinless fermions under consideration here 63,[75][76][77][78] . A commonality amongst these studies is that the information quantity in question (entanglement entropy, negativity, concurrence, purity, etc.)…”

Section: A Phase Transitions and Limiting Cases Of V /Tmentioning

confidence: 99%

Operationally accessible entanglement of one-dimensional spinless fermions

2019

View full text Add to dashboard Cite

For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.

show abstract

Section: A Phase Transitions and Limiting Cases Of V /Tmentioning

confidence: 99%

Operationally accessible entanglement of one-dimensional spinless fermions

2019

View full text Add to dashboard Cite

show abstract

“…It has a huge range of applications being able to properly describe copper-oxide materials related to the high-T c cuprate superconductors [1], conducting polymers [2], and organic charge-transfer salts [3]. The full EFM phase diagram has been studied for specific fillings by means of different techniques [4][5][6][7][8][9]. In particular, the repulsive interaction regime has been intensively investigated due to the presence of a phase with bond-order waves (BOW) [8], not predicted within single loop bosonization [10].…”

Section: Introductionmentioning

confidence: 99%

Non-local order parameters as a probe for phase transitions in the extended Fermi-Hubbard model

Barbiero

Fazzini

Montorsi

2017

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Abstract. The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local operators related to charge and spin fluctuations. The main advantage in using them is that, in contrast to usual local operators, their asymptotic average value is finite only in the appropriate gapped phases. This makes them powerful and accurate probes to detect quantum phase transitions. Our results indeed confirm that they are able to properly capture both the nature and the location of the transitions. Relevantly, this happens also for conducting phases with a spin gap, thus providing an order parameter for the identification of superconducting and paired superfluid phases.

show abstract

“…The 1D extended Hubbard model has been extensively studied, see e.g. [32][33][34][35]; here we limit attention to the well-known predictions that obtain from bosonization [30,31], expected to hold for sufficiently weak coupling. In 1D, electronic quasiparticles are ill-defined for arbitrarily weak interactions.…”

Section: B Electron-electron Interactionsmentioning

confidence: 99%

“…By contrast, we here gain control over loop corrections by tuning the band curvature in the ky-direction (through the parameter 1/n, which does not enter the scaling dimension of g, namely [g] = − , in d * = 1+ ) instead of artificially increasing the flavor number. 8 The Dirac-semimetal to band-insulator QCP in the uniaxially strained honeycomb lattice is achieved at the cost of C 3v sym-sively studied by analytical [30,31] and numerical [32][33][34][35] methods (see also Sec. VIII A).…”

Section: B Electron-electron Interactionsmentioning

confidence: 99%

Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension

Roy

Foster

2018

Phys. Rev. X

View full text Add to dashboard Cite

We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal and a symmetry-preserving band insulator. The electronic dispersion at this critical point is anisotropic (in unconventional scaling of thermodynamic and transport quantities. Because of the vanishing density of states [ϱðEÞ ∼ jEj 1/n ], this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions, the direct Dirac-semimetal to band-insulator transition can either (i) become a fluctuation-driven first-order transition (although unlikely in a particular microscopic model considered here, the anisotropic honeycomb lattice extended Hubbard model) or (ii) get avoided by an intervening broken-symmetry phase. We perform a controlled renormalization group analysis with the small parameter ϵ ¼ 1/n, augmented with a 1/n expansion (parametrically suppressing quantum fluctuations in the higher dimension) by perturbing away from the one-dimensional limit, realized by setting ϵ ¼ 0 and n → ∞. We identify charge density wave (CDW), antiferromagnet (AFM), and singlet s-wave superconductivity as the three dominant candidates for broken symmetry. The onset of any such order at strong coupling ð∼ϵÞ takes place through a continuous quantum phase transition across an interacting multicritical point, where the ordered phase, band insulator, Dirac, and anisotropic semimetals meet. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2)-symmetric quantum critical points separating the ASM from the AFM and superconducting orders, respectively. Our phase diagram shows an intriguing interplay among CDW, AFM, and s-wave paired states that can be germane for a uniaxially strained optical honeycomb lattice for ultracold fermion atoms, or the organic compound α-ðBEDT-TTFÞ 2 I 3 .

show abstract

Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model

Cited by 56 publications

References 42 publications

Operationally accessible entanglement of one-dimensional spinless fermions

Operationally accessible entanglement of one-dimensional spinless fermions

Non-local order parameters as a probe for phase transitions in the extended Fermi-Hubbard model

Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension

Contact Info

Product

Resources

About