Illustrating the Categorical Landau Paradigm in Lattice Models

TL;DR

This paper demonstrates how non-invertible (categorical) symmetries extend the Landau paradigm by providing a lattice model in (1+1)d where phase behavior is governed by these symmetries.

Contribution

It introduces a lattice model illustrating the role of non-invertible symmetries in phase transitions, expanding the Landau paradigm.

Findings

Gapped phases explained by non-invertible symmetry breaking

Phase transitions characterized by categorical symmetries

Provides a concrete (1+1)d lattice model example

Abstract

Recent years have seen the concept of global symmetry extended to non-invertible (or categorical) symmetries, for which composition of symmetry generators is not necessarily invertible. Such non-invertible symmetries lead to a generalization of the standard Landau paradigm. In this work we substantiate this framework by providing a (1+1)d lattice model, whose gapped phases and phase transitions can only be explained by symmetry breaking of non-invertible symmetries.