Entanglement entropy scaling laws and eigenstate typicality in free fermion systems

Lai, Hsin-Hua; Yang, Kun

doi:10.1103/physrevb.91.081110

Cited by 75 publications

(85 citation statements)

References 40 publications

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“…This has been one of the reasons that most of the studies were focused on the bipartite entanglement entropy of the ground states. Nevertheless, some typical behavior (volume-law) has been already observed for the excited states too, see Refs [33][34][35]. Some further analytical and numerical results were also obtained for the average of the entanglement entropy in [38,43,44] which support some sort of universality.…”

supporting

confidence: 53%

“…Then the entanglement entropy of the low-lying excited states in CFTs was calculated in [30,31]. For recent numerical calculations regarding the entanglement entropy of the excited states in the quantum spin chains and free fermions see [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. For further results on the entanglement entropy of the low-lying excited states in CFTs see [48][49][50][51][52][53][54].…”

mentioning

confidence: 99%

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Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Jafarizadeh

Rajabpour

2019

Phys. Rev. B

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We study general entanglement properties of the excited states of the one dimensional translational invariant free fermions and coupled harmonic oscillators. In particular, using the integrals of motion, we prove that these Hamiltonians independent of the gap (mass) has infinite excited states that can be described by conformal field theories with integer or half-integer central charges. In the case of free fermions, we also show that because of the huge degeneracy in the spectrum, even a gapless Hamiltonian can have excited states with an area-law. Finally, we study the universal average entanglement entropy over eigenstates of the Hamiltonian of the free fermions introduced recently in [L. Vidmar, et al., Phys. Rev. Lett. 119, 020601 (2017)]. In particular, using a duality relation, we propose a method which can be useful for experimental measurement of the universal average entanglement entropy. Part of our conclusions can be extended to the quantum spin chains that are associated with the free fermions via Jordan-Wigner(JW) transformation.

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supporting

confidence: 53%

mentioning

confidence: 99%

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Jafarizadeh

Rajabpour

2019

Phys. Rev. B

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“…32 (see also Refs. 33 and 34) that if a "coarse-grained" occupation number n c (k), defined through some suitable averaging procedure of the microscopic variables n k in a shell of (infinitesimal) width δk around k is considered, then the most probable form of n c (k) appears thermal (i.e.…”

Section: Properies Of Typical Eigenstatesmentioning

confidence: 99%

“…24) by extending the arguments of Ref. 32, taking into account the additional conservation laws which specify the generalized Microcanonical ensembles in terms of the Bogoluibov fermion occupations n k .…”

Section: Sampling Atypical Eigenstatesmentioning

confidence: 99%

Eigenstate Gibbs ensemble in integrable quantum systems

et al. 2016

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The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of relevant conserved quantities. In a generic system, only the energy plays that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and hence the reduced density matrix requires specification of an infinite number of parameters (Generalized Gibbs Ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density, that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e. requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately truncated Generalized Gibbs Ensembles. We further show that the presence of these rare eigenstates differentiates the model from the generic (non-integrable) case and leads to the system being described by a Generalized Gibbs Ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a Gibbs-like eigenstate of the pre-quench Hamiltonian.

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“…Recently more attention has been focused on entanglement entropy of highly excited states (namely states with finite excitation energy density), including free fermion systems [7][8][9][10] . In the meantime, a new study extended the idea of RSRG to include calculation of excited eigenstate of random spin chains, which is named RSRG-X method 11 .…”

Section: −Hmentioning

confidence: 99%

Entanglement spectrum and entangled modes of highly excited states in randomXXspin chains

Pouranvari

Yang

2015

Phys. Rev. B

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We examine the real space renormalization group method of finding excited eigenstate (RSRG-X) of the XX spin-1/2 chain, from entanglement perspectives. Eigenmodes of entanglement Hamiltonian, especially the maximally entangled mode and corresponding entanglement energies are studied and compared with predictions of RSRG-X. Our numerical results demonstrate the accuracy of the RSRG-X method in the strong disorder limit, and quantify its error when applied to weak disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.

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Entanglement entropy scaling laws and eigenstate typicality in free fermion systems

Cited by 75 publications

References 40 publications

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Eigenstate Gibbs ensemble in integrable quantum systems

Entanglement spectrum and entangled modes of highly excited states in randomXXspin chains

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