On the real-time evolution of pseudo-entropy in 2d CFTs

TL;DR

This paper investigates the real-time dynamics of pseudo-entropy in 2D conformal field theories, revealing symmetries, late-time behaviors, and conditions for real-valued pseudo-entropy in various operator excitation scenarios.

Contribution

It provides a detailed analysis of pseudo-Renyi entropy evolution in 2D CFTs, highlighting new symmetries and explicit late-time formulas for linear combinations of operators.

Findings

Pseudo-Renyi entropy exhibits specific symmetries related to subsystem and operator positions.

Late-time pseudo-Renyi entropy for linear combinations depends on coefficients and operator R extquoteright{}s entropy.

Certain spatial configurations keep pseudo-entropy real throughout evolution.

Abstract

In this work, we study the real-time evolution of pseudo-(R\'enyi) entropy, a generalization of entanglement entropy, in two-dimensional conformal field theories (CFTs). We focus on states obtained by acting primary operators located at different space points or their linear combinations on the vacuum. We show the similarities and differences between the pseudo-(R\'enyi) entropy and entanglement entropy. For excitation by a single primary operator, we analyze the behaviors of the 2nd pseudo-R\'enyi entropy in various limits and find some symmetries associated with the subsystem and the positions of the insertion operators. For excitation by linear combinations, the late time limit of the $n$th pseudo-R\'enyi entropy shows a simple form related to the coefficients of the combinations and R\'enyi entropy of the operators, which can be derived by using the Schmidt decomposition. Further, we find two kinds of particular spatial configurations of insertion operators in one of which the pseudo-(R\'enyi) entropy remains real throughout the time evolution.