Classification of Matrix Product States with a Local (Gauge) Symmetry

TL;DR

This paper classifies Matrix Product States that exhibit local gauge invariance, revealing their structure and connections to known gauging procedures, thereby advancing the understanding of symmetric tensor network states in gauge theories.

Contribution

It provides a comprehensive classification of MPS with local gauge symmetry, identifying their structures and relation to known gauging methods.

Findings

Identifies known and new gauge-invariant MPS constructions

Analyzes the tensor structures underlying local gauge invariance

Connects MPS gauge invariance to gauging procedures in quantum systems

Abstract

Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode symmetries on the level of a single building block (tensor), and hence they provide a natural playground for the study of symmetric systems. In particular, recent works have proposed to use MPS (and higher dimensional tensor networks) for the study of systems with local symmetry that appear in the context of gauge theories. In this work we classify MPS which exhibit local invariance under arbitrary gauge groups. We study the respective tensors and their structure, revealing known constructions that follow known gauging procedures, as well as different, other types of possible gauge invariant states.