Eigenstate thermalization hypothesis in conformal field theory

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong

doi:10.1088/1742-5468/aab020

Cited by 125 publications

(199 citation statements)

References 23 publications

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“…2 It has been pointed out that this random behavior is not exactly correct in generic chaotic quantum systems because R nm satisfy various constraints [28,34]. Our analysis for generic CFTs is not affected by this issue as we consider averaged quantities.…”

Section: Comparison With Ethmentioning

confidence: 94%

“…Remember that the averageM in the above means that for all states with the energy E i.e.M ¼ e −NSðEÞ P A 1 ;A 2 ;…;A N M. When N is odd, we can obtain the same estimation (28) from the ETH ansatz (22) by replacing one of e −SðEÞ=2 R nm with δ n;m in the averaged random correlation function. In this way, the CFT result (27) reproduces the random matrix result (28) based on the ETH ansatz for these correlation functions.…”

Section: E Torus Multipoint Functions and Modular Invariancementioning

confidence: 96%

“…The latter analysis provides new universal properties on the one-point functions on a disk or equally the coefficients of boundary states. Our analysis below focuses only on the exponential contributions neglecting the polynomial factor of the energy of relevant states, which is denoted by the symbol ∼: Refer to [27][28][29][30][31][32][33] for earlier arguments on ETH in CFTs.…”

Section: Introductionmentioning

confidence: 99%

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Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories

2018

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Section: Comparison With Ethmentioning

confidence: 94%

Section: E Torus Multipoint Functions and Modular Invariancementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories

2018

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“…Recently it has been shown in [12] that the subsystem ETH is related to the a local form of ETH which states off-diagonal matrix elements of energy eigenstates are entropically suppressed. Moreover, for CFTs another measure for equivalence for density matrices, is…”

Section: Subsystem Eth In 2d Cftsmentioning

confidence: 99%

Thermality of eigenstates in conformal field theories

et al. 2017

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The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-d conformal field theories, consisting of quasi-primaries of the identity module, which satisfy the hypothesis only at the leading order in large central charge. In the context of subsystem ETH, this plays a role in the deviation of the reduced density matrices, corresponding to a finite energy density eigenstate from its hypothesized thermal approximation. The universal deviation in terms of the square of the trace-square distance goes as the 8th power of the subsystem fraction and is suppressed by powers of inverse central charge (c). Furthermore, the non-universal deviations from subsystem ETH are found to be proportional to the heavy-light-heavy structure constants which are typically exponentially suppressed in h/c, where h is the conformal scaling dimension of the finite energy density state. We also examine the effects of the leading finite size corrections.

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“…Note added: when we are preparing the draft, there appears the paper [26] in ArXiv that has some overlaps with our paper.…”

Section: Jhep11(2016)116mentioning

confidence: 99%

Thermality and excited state Rényi entropy in two-dimensional CFT

Lin

Wang

Zhang

2016

J. High Energ. Phys.

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We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.

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Eigenstate thermalization hypothesis in conformal field theory

Cited by 125 publications

References 23 publications

Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories

Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories

Thermality of eigenstates in conformal field theories

Thermality and excited state Rényi entropy in two-dimensional CFT

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