Entropic order parameters and topological holography

TL;DR

This paper demonstrates how the symmetry topological field theory framework offers an intuitive way to understand entropic order parameters, especially in phases with broken symmetries, using examples of group and non-invertible symmetries.

Contribution

It introduces a novel interpretation of entropic order parameters within the topological holography framework, highlighting the role of information-theoretic perspectives in symmetry breaking.

Findings

SymTFT provides a natural framework for entropic order parameters.

Distinguishability of vacua linked to non-invertible symmetry breaking.

Operators excluded from observation reveal symmetry breaking details.

Abstract

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken symmetries. Various examples of group and non-invertible symmetries are studied. In particular, the origin of the distinguishability of the vacua resulting from spontaneously broken non-invertible symmetries is made manifest with an information-theoretic perspective, where certain operators in the SymTFT are excluded from observation.