Explicit tensor network representation for the ground states of string-net models

TL;DR

This paper presents an explicit tensor network representation for the ground states of string-net models, emphasizing the role of the fat lattice and tensor categories in understanding topological phases.

Contribution

It introduces a straightforward tensor network construction for string-net ground states based on tensor category data, clarifying the role of the fat lattice.

Findings

Ground states expressed as tensor networks from tensor category data

Highlights importance of fat lattice in understanding models

Simplifies analysis of topological phases

Abstract

The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor categories. The construction highlights the importance of the fat lattice to understand these models.