Entropic Order Parameters for Categorical Symmetries in 2D-CFT

TL;DR

This paper introduces an information-theoretic order parameter based on quantum relative entropy to detect and characterize the breaking of categorical symmetries in (1+1)-dimensional rational conformal field theories, especially at phase transitions.

Contribution

It proposes a novel entropic order parameter using quantum relative entropy that depends on quantum dimensions, providing a new way to identify symmetry-breaking phases in RCFTs.

Findings

Relative entropy depends on quantum dimensions at high temperature

Order parameter characterizes different broken phases

Method applicable to (1+1)-d theories with categorical symmetries

Abstract

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1 + 1)-d rational conformal field theories (RCFT). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1 + 1)-d theories with categorical symmetries.