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arXiv:2404.04805 · Journal of High Energy Physics

Logarithmic singularities of Renyi entropy as a sign of chaos?

Norihiro Iizuka, Mitsuhiro Nishida

Published Oct 4, 2024• 1 citation
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Abstract

A bstract We propose that the logarithmic singularities of the Renyi entropy of local-operator-excited states for replica index n can be a sign of quantum chaos. As concrete examples, we analyze the logarithmic singularities of the Renyi entropy in various two-dimensional conformal field theories. We show that there are always logarithmic singularities of the Renyi entropy in holographic CFTs, but no such singularities in free and rational CFTs. These singularities of the Renyi entropy are also related to the logarithmic time growth of the Renyi entropy at late times.

DOI
10.1007/jhep10(2024)043

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A bstract We propose that the logarithmic singularities of the Renyi entropy of local-operator-excited states for replica index n can be a sign of quantum chaos. As concrete examples, we analyze the logarithmic singularities of the Renyi entropy in various two-dimensional conformal field theories. We show that there are always logarithmic singularities of the Renyi entropy in holographic CFTs, but no such singularities in free and rational CFTs. These singularities of the Renyi entropy are also related to the logarithmic time growth of the Renyi entropy at late times.
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 ΔSA(n)≃nc24(n−1) \varDelta {S}_A^{(n)}\simeq \frac{nc}{24\left(n-1\right)} ΔSA(n)​≃24(n−1)nc​ log t. Our numerical results also confirm existing analytical results using the HHLL approximation.
A bstract In this paper, we explore the concept of pseudo Rényi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically, when the operators are positioned in the left and right Rindler wedges respectively, we discover that the logarithmic term of the pseudo Rényi entropy is necessarily real. In other cases, the result might be complex. We provide direct evaluations of specific examples within 2-dimensional conformal field theories (CFTs). Furthermore, we establish a connection between these findings and the pseudo-Hermitian condition. Our analysis reveals that the reality or complexity of the logarithmic term of pseudo Rényi entropy can be explained through this pseudo-Hermitian framework. Additionally, we investigate the divergent term of the pseudo Rényi entropy. Interestingly, we observe a universal divergent term in the second pseudo Rényi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For n -th pseudo Rényi entropy ( n ≥ 3), the divergent term is intricately related to the specific details of the underlying theory.
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In this paper, we study Renyi and von Neumann entanglement entropy of excited states created by local operators in large-|NNN| (or large-central-charge) conformal field theories (CFTs). First we point out that a naive large-|NNN| expansion can break down for the von Neumann entanglement entropy, while it does not for the Renyi entanglement entropy. This happens even for the excited states in free Yang–Mills theories. Next, we analyze strongly coupled large-|NNN| CFTs from both the field-theoretic and holographic viewpoints. We find that the Renyi entanglement entropy of the excited state, produced by a local operator, grows logarithmically under its time evolution and its coefficient is proportional to the conformal dimension of the local operator.
Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.