Self-$G$-ality in 1+1 dimensions

TL;DR

This paper investigates topological manipulations with dual symmetries in 1+1D systems, establishing constraints on ground states and linking lattice models to IR theories through self-$G$-ality structures.

Contribution

It introduces the concept of self-$G$-ality for topological manipulations, providing new constraints and insights into symmetry enhancements in 1+1D systems.

Findings

Derived LSM-type constraints on ground states.

Linked self-$G$-ality structures to IR critical theories.

Analyzed concrete lattice models exhibiting self-$G$-ality.

Abstract

We explore topological manipulations in one spatial dimension, which are defined for a system with a global symmetry and map the system to another one with a dual symmetry. In particular, we discuss fusion category symmetries enhanced by the invariance of the actions of topological manipulations, i.e., self-$G$-alities for topological manipulations. Based on the self-$G$-ality conditions, we provide LSM-type constraints on the ground states of many-body Hamiltonians. We clarify the relationship between different enhanced symmetries and how they are further enhanced when they meet. We explore concrete lattice models for such self-$G$-alities and identify how the self-$G$-ality structures match the IR critical theories.