Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Ercolessi, Elisa; Naldesi, Piero; Taddia, Luca; Vodola, Davide

doi:10.1103/physrevb.89.104303

Cited by 79 publications

(45 citation statements)

References 55 publications

(65 reference statements)

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“…Besides the determination of order parameters, quantities such as gaps, spatial correlation functions, and structure factors are commonly used to determine the quantum critical points of several models. Remarkably, a few years ago it was realized that entanglement plays a fundamental role in critical phenomena and that different measures of entanglement can be used to determine the location of several types of QPTs [9][10][11][12][13][14][15][16][17][18][19][20][21]. Furthermore, the relation of Bell inequalities and criticality has been recently explored [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

et al. 2016

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In the present paper we introduce a way of identifying quantum phase transitions of many-body systems by means of local time correlations and Leggett-Garg inequalities. This procedure allows us to experimentally determine the quantum critical points not only of finite-order transitions but also those of infinite order, as the Kosterlitz-Thouless transition that is not always easy to detect with current methods. By means of simple analytical arguments for a general spin-1/2 Hamiltonian, and matrix product simulations of one-dimensional XXZ and anisotropic XY models, we argue that finite-order quantum phase transitions can be determined by singularities of the time correlations or their derivatives at criticality. The same features are exhibited by corresponding Leggett-Garg functions, which noticeably indicate violation of the Leggett-Garg inequalities for early times and all the Hamiltonian parameters considered. In addition, we find that the infinite-order transition of the XXZ model at the isotropic point can be revealed by the maximal violation of the Leggett-Garg inequalities. We thus show that quantum phase transitions can be identified by purely local measurements and that many-body systems constitute important candidates to observe experimentally the violation of Leggett-Garg inequalities.

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Section: Introductionmentioning

confidence: 99%

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

et al. 2016

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“…In a time-dependent setting one could analyze how this entanglement avalanche is affected by non-adiabatic dynamics during a sweep through the critical point. In fact, the number of non-zero values for the transverse Ising chain has been seen to grow up to four in the case of equal bipartition 51 , such that the approximations applied here could survive further.…”

Section: Conclusion and Discussionmentioning

confidence: 91%

Avalanche of entanglement and correlations at quantum phase transitions

Krutitsky

Osterloh

Schützhold

2017

Sci Rep

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We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J = ∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should be taken into account in the approximations starting from a mean-field limit.

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“…In particular we would like to understand possible universal scaling of the entropy as a function of the quench rate. While some results about such scaling behavior are known in solvable and integrable field theories [28][29][30][31][32] , very little is known in strongly coupled systems. In the past, holographic methods have been useful to understand scaling of one point functions in various regimes…”

Section: Jhep09(2017)016mentioning

confidence: 99%

Holographic entanglement entropy of a 1 + 1 dimensional p-wave superconductor

Das

Fujita

Kim

2017

J. High Energ. Phys.

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We examine the behavior of entanglement entropy S EEA of a subsystem A in a fully backreacted holographic model of a 1 + 1 dimensional p wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size l smaller than a critical size l c1 , S EE A continues to increase as a function of the charge density as we cross the phase transition. When l lies between l c1 and another critical size l c2 the entanglement entropy displays a nonmonotonic behavior, while for l > l c2 it decreases monotonically. At large charge densities S EE A appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.

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Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Cited by 79 publications

References 55 publications

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Avalanche of entanglement and correlations at quantum phase transitions

Holographic entanglement entropy of a 1 + 1 dimensional p-wave superconductor

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