Models for gapped boundaries and domain walls

TL;DR

This paper introduces lattice models for 2D topological phases with gapped boundaries and domain walls, linking physical models to tensor category theory.

Contribution

It constructs a class of lattice models with gapped boundaries and domain walls using tensor categories and module categories, establishing a dictionary between physics and category theory.

Findings

Bulk and boundary excitations are gapped in the models.

Domain walls are transparent if the associated categories are Morita equivalent.

Provides a categorical framework for understanding topological boundary phenomena.

Abstract

We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $\calC$. We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.