Microscopic origin of thermodynamic entropy in isolated systems

Deutsch, J. M.; Li, Haibin; Sharma, Auditya

doi:10.1103/physreve.87.042135

Cited by 133 publications

(152 citation statements)

References 26 publications

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“…The entanglement entropy grows with time; the initial growth for almost all cuts in the equatorial region is approximately linear. This is seen explicitly in figure 7(b), where the entanglement entropy for the half-partition (l At long times, the entanglement entropy profile eventually settles to values consistent with the entanglement entropy in high-energy eigenstates, or equivalently, with the entanglement entropy in random or 'thermal' eigenstates [118][119][120][121][122][123][124][125]. This is seen in the right panel, where we have plotted the orbital entanglement entropy profiles (entanglement entropy versus l A ) for the 20 eigenstates that are closest in energy to the expectation energy of the time-evolving (or initial) state.…”

Section: Entanglement Dynamicsmentioning

confidence: 84%

Dynamics and level statistics of interacting fermions in the lowest Landau level

et al. 2018

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We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g.in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian orthogonal ensemble) can appear in many cases despite the lack of time-reversal symmetry.

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Section: Entanglement Dynamicsmentioning

confidence: 84%

Dynamics and level statistics of interacting fermions in the lowest Landau level

et al. 2018

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“…In a thermal state, S n,A exhibits a volume-law behaviour S n,A ∝ L d . For S vN , the prefactor of the volume-law is the same as that of the thermal entropy, i.e., the von Neumann entanglement entropy becomes the thermodynamic entropy at finite temperature [41][42][43]. The mutual information between two subsystems is defined for the typical geometry depicted in Fig.…”

Section: Entanglement Entropies Mutual Information and Logarithmicmentioning

confidence: 99%

Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature T and of the quantum parameter g, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any g and T , the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of g, T , the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any g, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough T . The vanishing of the negativity defines a "death line", which we characterise analytically at small g. Importantly, for any finite T the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit T → 0. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

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“…Discussions of the extensivity or the lack thereof of entanglement entropy have abounded [17][18][19][20][21][22][23] in recent times, in the context of the celebrated area law [24][25][26]. However, the relationship between entanglement entropy and thermodynamic entropy has only been scantily covered [27]. In this Letter, we demonstrate, with the aid of a specific example, that a systematic study of this relationship is an illuminating diagnostic for a class of quantum phase transitions.…”

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confidence: 79%

Entanglement and thermodynamic entropy in a clean many-body-localized system

Bhakuni

Sharma

2020

J. Phys.: Condens. Matter

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Whether or not the thermodynamic entropy is equal to the entanglement entropy of an eigenstate, is of fundamental interest, and is closely related to the 'Eigenstate thermalization hypothesis (ETH)'. However, this has never been exploited as a diagnostic tool in many-body localized systems. In this work, we perform this diagnostic test on a clean interacting system (subjected to a static electric field) that exhibits three distinct phases: integrable, non-integrable ergodic and non-integrable many-body-localized (MBL). We find that in the non-integrable ergodic phase, the equivalence between the thermodynamic entropy and the entanglement entropy of individual eigenstates, holds. In sharp contrast, in the integrable and non-integrable MBL phases, the entanglement entropy shows large eigenstate-to-eigenstate fluctuations, and differs from the thermodynamic entropy. Thus the non-integrable MBL phase violates ETH similar to an integrable system; however, a key difference is that the magnitude of the entanglement entropy in the MBL phase is significantly smaller than in the integrable phase, where the entanglement entropy is of the same order of magnitude as in the non-integrable phase, but with a lot of eigenstate-to-eigenstate fluctuations. Quench dynamics from an initial CDW state independently supports the validity of the ETH in the ergodic phase and its violation in the MBL phase.

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Microscopic origin of thermodynamic entropy in isolated systems

Cited by 133 publications

References 26 publications

Dynamics and level statistics of interacting fermions in the lowest Landau level

Dynamics and level statistics of interacting fermions in the lowest Landau level

Entanglement and classical fluctuations at finite-temperature critical points

Entanglement and thermodynamic entropy in a clean many-body-localized system

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