Entanglement dynamics after quantum quenches in generic integrable  systems

Alba, Vincenzo; Calabrese, Pasquale

doi:10.21468/scipostphys.4.3.017

Cited by 231 publications

(351 citation statements)

References 191 publications

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“…As a final remark, we have seen that the agreement of the CFT predictions with the data of the true spin chains is quite scarce if we do not linearize the dispersion relation. It would be interesting, for the spin chains considered here (and more generically for an arbitrary integrable system), to find a procedure to take into account the contributions of the various excited modes with different velocities, for example on the lines of what has been done for the entanglement entropy after a global quantum quench [70,71].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

J. High Energ. Phys.

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We investigate the time evolution of the subsystem trace distance and Schatten distances after local operator quenches in two-dimensional conformal field theory (CFT) and in one-dimensional quantum spin chains. We focus on the case of a subsystem being an interval embedded in the infinite line. The initial state is prepared by inserting a local operator in the ground state of the theory. We only consider the cases in which the inserted local operator is a primary field or a sum of several primaries. While a nonchiral primary operator can excite both left-moving and rightmoving quasiparticles, a holomorphic primary operator only excites a right-moving quasiparticle and an anti-holomorphic primary operator only excites a left-moving one. The reduced density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to the RDM of the interval without any quasiparticles. Moreover, the RDMs of two intervals hosting quasiparticles at different positions are also orthogonal to each other. We calculate numerically the entanglement entropy, Rényi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains. These results match the CFT predictions in the proper limit.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

J. High Energ. Phys.

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“…where we used that, thanks to Theorem 1, the matrix S in (27) can be chosen equal to the identity. This circuit can be further contracted by repeated use of the initial state's solvability condition (27) combined with the dual-unitarity property (10). Two different results are obtained depending on whether or not 2t is larger than .…”

Section: The Entanglement Growthmentioning

confidence: 99%

Exact dynamics in dual-unitary quantum circuits

et al. 2020

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We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of "solvable" matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size reaches infinite temperature after a time t ∝ , irrespective of the presence of conserved quantities, the light-cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of non-solvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

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“…The quasi-particle posits that for all integrable systems, when the system is excited above the ground state, the entanglement dynamics can be fully accounted for by tracking the trajectories of local "quasi-particles" [24][25][26][27]. For a global quench, quasi-particle pairs are created homogeneously across the entire system.…”

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confidence: 99%

Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

Kudler-Flam

Kusuki

Ryu

2020

J. High Energ. Phys.

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We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone bootstrap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the "line-tension picture," motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational

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Entanglement dynamics after quantum quenches in generic integrable systems

Cited by 231 publications

References 191 publications

Subsystem distance after a local operator quench

Subsystem distance after a local operator quench

Exact dynamics in dual-unitary quantum circuits

Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

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