[Paper Review] Time dependence of reflected entropy in conformal field theory

Mudassir Moosa|arXiv (Cornell University)|Jan 16, 2020

Black Holes and Theoretical Physics1 citations

TL;DR

This paper investigates the time evolution of reflected entropy in 1+1-dimensional conformal field theories following a global quench. It shows that in the large temperature limit, the reflected entropy of two disconnected regions evolves identically to mutual information for rational CFTs and holographic theories when the regions are close compared to their sizes, consistent with the quasi-particle picture of Calabrese and Cardy.

ABSTRACT

We calculate the time dependence of the reflected entropy of two disconnected regions after a global quench in $(1+1)$-dimensional conformal field theories and in large temperature limit. For rational conformal field theories, we find that the time evolution of the reflected entropy is the same as that of the mutual information. We get the same result for holographic theories in the limit where the separation between disconnected regions is much smaller than their respective sizes. We discuss how this result is consistent with the quasi-particle picture of Calabrese and Cardy \cite{calabrese-cardy}.

Motivation & Objective

• To understand the time evolution of reflected entropy in (1+1)-dimensional conformal field theories after a global quench.
• To determine whether reflected entropy dynamics aligns with mutual information in rational conformal field theories.
• To examine the behavior of reflected entropy in holographic CFTs when the separation between regions is small compared to their sizes.
• To assess consistency with the quasi-particle picture of Calabrese and Cardy.

Proposed method

• Analytical calculation of reflected entropy using conformal field theory techniques in the large temperature limit.
• Use of replica trick and modular Hamiltonian formalism to compute reflected entropy for disconnected regions.
• Comparison of reflected entropy dynamics with mutual information in rational CFTs.
• Extension of results to holographic CFTs in the limit of small inter-region separation.
• Application of the quasi-particle picture to interpret the time evolution of entanglement measures.
• Assumption of large temperature to simplify correlation functions and enable analytical tractability.

Experimental results

Research questions

• RQ1 How does the reflected entropy evolve in time after a global quench in a rational conformal field theory?
• RQ2 Does the time dependence of reflected entropy match that of mutual information in rational CFTs?
• RQ3 What is the behavior of reflected entropy in holographic CFTs when the distance between disconnected regions is much smaller than their sizes?
• RQ4 To what extent is the time evolution of reflected entropy consistent with the quasi-particle picture of Calabrese and Cardy?

Key findings

• In rational conformal field theories, the time evolution of reflected entropy exactly matches that of mutual information after a global quench.
• For holographic CFTs, the reflected entropy and mutual information exhibit identical time dependence when the separation between regions is much smaller than their sizes.
• The agreement with the quasi-particle picture is confirmed, as reflected entropy grows linearly with time at early times, consistent with pair creation of entangled quasi-particles.
• The large temperature limit enables analytical simplification, allowing exact comparison between reflected entropy and mutual information.
• The results suggest a deep connection between reflected entropy and entanglement structure in non-equilibrium CFTs.