R\'enyi entropy of locally excited states with thermal and boundary effect in 2D CFTs

TL;DR

This paper investigates the behavior of R'enyi entropy for locally excited states in 2D CFTs, considering thermal and boundary effects, revealing boundary influence on entropy evolution and its relation to quantum dimensions.

Contribution

It provides a detailed analysis of R'enyi entropy in 2D CFTs with thermal and boundary effects, including a quasi-particle interpretation and boundary condition independence.

Findings

R'enyi entropy evolution is unaffected by boundary conditions.

Boundary modifies the time evolution of R'enyi entropy.

In rational CFTs, R'enyi entropy matches the log of quantum dimension during certain periods.

Abstract

We study R\'enyi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly we consider locally excited states obtained by acting primary operators on a thermal state in low temperature limit. The R\'enyi entropy is summation of contribution from thermal effect and local excitation. Secondly, we mainly study the R\'enyi entropy of locally excited states in 2D CFT with a boundary. We show that the evolution of R\'enyi entropy does not depend on the choice of boundary conditions and boundary will change the time evolution of R\'enyi entropy. Moreover, in 2D rational CFTs with a boundary, we show that the R\'enyi entropy always coincides with the log of quantum dimension of the primary operator during some periods of the evolution. We make use of a quasi-particle picture to understand this phenomenon. In terms of quasi-particle interpretation, the boundary behaves as an infinite potential barrier which reflects any energy moving towards the boundary.