Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

Giulio, Giuseppe Di; Arias, Raúl; Tonni, Erik

doi:10.1088/1742-5468/ab4e8f

Cited by 70 publications

(104 citation statements)

References 146 publications

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“…The quasi-particle picture naturally suggests an entanglement contour that was originally considered in Ref. [114]. This is because the quasi-particles are additive in the von Neumann entropy, so the contour is simply the contribution of the quasi-particles from the given subregion…”

Section: Quantum Quench and Thermalizationmentioning

confidence: 99%

The negativity contour: a quasi-local measure of entanglement for mixed states

2020

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In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the negativity contour, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.1

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Section: Quantum Quench and Thermalizationmentioning

confidence: 99%

The negativity contour: a quasi-local measure of entanglement for mixed states

2020

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“…The entanglement contour [72] is a quasi-local notion of entanglement that may be useful for understanding dynamics of quantum and classical information locally. For example, it has been studied following quantum quenches in both integrable and nonintegrable conformal field theories [72][73][74]. It would thus be interesting to study (state-independent) scrambling with the entanglement contour (or negativity contour [73,75,76]).…”

Section: Future Directionsmentioning

confidence: 99%

Quantum vs. classical information: operator negativity as a probe of scrambling

2020

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We consider the logarithmic negativity and related quantities of time evolution operators. We study free fermion, compact boson, and holographic conformal field theories (CFTs) as well as numerical simulations of random unitary circuits and integrable and chaotic spin chains. The holographic behavior strongly deviates from known non-holographic CFT results and displays clear signatures of maximal scrambling. Intriguingly, the random unitary circuits display nearly identical behavior to the holographic channels. Generically, we find the "line-tension picture" to effectively capture the entanglement dynamics for ergodic systems and the "quasi-particle picture" for integrable systems. With this motivation, we propose an effective "line-tension" that captures the dynamics of the logarithmic negativity in ergodic systems in the spacetime scaling limit. We compare the negativity and mutual information leading us to find distinct dynamics of quantum and classical information. The "spurious entanglement" we observe may have implications on the "simulatability" of quantum systems on classical computers. Finally, we elucidate the connection between the operation of partially transposing a density matrix in conformal field theory and the entanglement wedge cross section in Anti-de Sitter space using geodesic Witten diagrams. 1 arXiv:1906.07639v1 [hep-th]

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“…Recently, several papers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] studied the so-called entanglement contour [5], which is a function that characterizes how much each degree of freedom in a region A contributes to the entanglement entropy S A . In other words, consider a quantum field theory in d dimensions (in this paper d means the dimension of space-time), the entanglement contour is a density function of entanglement entropy that depends on A and satisfies…”

Section: Introductionmentioning

confidence: 99%

Formulas for partial entanglement entropy

Wen

2020

Phys. Rev. Research

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The partial entanglement entropy (PEE) s A (A i) characterizes how much the subset A i of A contribute to the entanglement entropy S A. We find one additional physical requirement for s A (A i), which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincaré invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the PEE proposal is a solution, the PEE proposal is justified for Poincaré invariant theories.

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Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

Cited by 70 publications

References 146 publications

The negativity contour: a quasi-local measure of entanglement for mixed states

The negativity contour: a quasi-local measure of entanglement for mixed states

Quantum vs. classical information: operator negativity as a probe of scrambling

Formulas for partial entanglement entropy

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