Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects

Stéphan, Jean-Marie; Dubail, Jérôme

doi:10.1088/1742-5468/2011/08/p08019

Cited by 150 publications

(273 citation statements)

References 63 publications

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“…There is still a L −1 log L correction in this case, but intriguingly, it disappears after analytic continuation to real time. However, we show that a slight modification of the Loschmidt echo-dubbed "detector" in [32]-preserves the correction. We finish with some concluding remarks in Sec.…”

Section: Organization Of the Manuscriptmentioning

confidence: 75%

“…Such behavior has been studied in detail in Ref. [32], for the entanglement entropy (EE) and the logarithmic Loschmidt echo (LLE). Recall that the Rényi entanglement entropy (REE) is defined as…”

Section: Time Evolution Following a Local Quenchmentioning

confidence: 92%

“…It is possible to circumvent this difficulty, and show that the logarithmic term we are investigating does appear in real time. To do so, we study a modified version of the LLE, called "Detector" in [32]. It is defined as…”

Section: The Loschmidt Echomentioning

confidence: 99%

“…The leading order of the one-point function was computed in [32], and we wish to use our result in Sec. 2.5 for the subleading logarithmic correction.…”

Section: Entanglement Entropymentioning

confidence: 99%

“…Like in the more complicated case of the "swap" quench, one can be interested in measuring the overlap between the two ground states of H and H . Let us refer to this local quench as the "cut-and-glue" quench; it is a problem that has been studied in recent papers [56,55,15,32]. Let us emphasize that the overlap between the two ground states H and H is not a Rényi entropy like in the case of the "swap" quench.…”

Section: Appendix A2 Action Of the Swap Operator On A Local Hamiltomentioning

confidence: 99%

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Logarithmic corrections to the free energy from sharp corners with angle 2π

Stéphan¹,

Dubail²

2013

J. Stat. Mech.

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Abstract. We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case of an angle 2π, we find that there is an unusual correction of the form L −1 log L, where L is a typical length scale in the system. This correction also affects the one-point function of an operator near the corner. The prefactor can be seen as semi-universal, in the sense that it depends on a single non-universal quantity, the extrapolation length. Once this ultraviolet cutoff is known, the term is entirely fixed by the geometry of the system, and the central charge of the CFT. Such a corner appears for example in the bipartite fidelity of a one-dimensional quantum system at criticality, which allows for several numerical checks in free fermions systems. We also present an exact result in the XX and Ising chains that confirms this analysis. Finally, we consider applications to the time evolution of the (logarithmic) Loschmidt echo and the entanglement entropy following a local quantum quench. Due to subtle issues in analytic continuation, we find that the logarithmic term in imaginary time transforms into a time-dependent L −2 correction for the entanglement entropy, and a L −2 log L term for the Loschmidt echo.

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Section: Organization Of the Manuscriptmentioning

confidence: 75%

Section: Time Evolution Following a Local Quenchmentioning

confidence: 92%

Section: The Loschmidt Echomentioning

confidence: 99%

“…The leading order of the one-point function was computed in [32], and we wish to use our result in Sec. 2.5 for the subleading logarithmic correction.…”

Section: Entanglement Entropymentioning

confidence: 99%

Section: Appendix A2 Action Of the Swap Operator On A Local Hamiltomentioning

confidence: 99%

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Logarithmic corrections to the free energy from sharp corners with angle 2π

Stéphan¹,

Dubail²

2013

J. Stat. Mech.

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Renyi entropy for local quenches in 2D CFT from numerical conformal blocks

Kusuki

Takayanagi

2018

J. High Energ. Phys.

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Abstract:We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of log t term. Our analysis covers the entire parameter regions with respect to the replica number n and the conformal dimension h O of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikov's recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge c, drastically changes when the dimensions of external primary states reach the value c/32. In particular, when h O ≥ c/32 and n ≥ 2, we find a new universal formula ∆S (n)A ≃ nc 24(n−1) log t. Our numerical results also confirm existing analytical results using the HHLL approximation.

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Holographic entanglement entropy from 2d CFT: heavy states and local quenches

Asplund

Bernamonti

Galli

et al. 2015

J. High Energ. Phys.

255

419

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Abstract:We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both highenergy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

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Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects

Cited by 150 publications

References 63 publications

Logarithmic corrections to the free energy from sharp corners with angle 2π

Logarithmic corrections to the free energy from sharp corners with angle 2π

Renyi entropy for local quenches in 2D CFT from numerical conformal blocks

Holographic entanglement entropy from 2d CFT: heavy states and local quenches

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