# Symmetry reduction induced by anyon condensation: a tensor network approach

## TL;DR

This paper explores how anyon condensation induces symmetry reduction in topological phases using tensor network methods, revealing connections between gauge symmetries and global symmetries in both 2D and 1D systems.

## Contribution

It introduces a tensor network framework to analyze symmetry reduction caused by anyon condensation, linking topological order to symmetry properties in PEPS and MPS.

## Key findings

- Symmetry reduction from local gauge to global on-site symmetry in topological phases.
- Application of symmetry reduction concepts to one-dimensional systems with MPS.
- Detailed analysis of $ ext{Z}_2$ on-site symmetry case.

## Abstract

Topological ordered phases are related to changes in the properties of their quasi-particle excitations (anyons). We study these relations in the framework of projected entanglement pair states (\textsf{PEPS}) and show how condensing and confining anyons reduces a local gauge symmetry to a global on-site symmetry. We also study the action of this global symmetry over the quasiparticle excitations. As a byproduct, we observe that this symmetry reduction effect can be applied to one-dimensional systems as well, and brings about appealing physical interpretations on the classification of phases with symmetries using matrix product states (\textsf{MPS}). The case of $\mathbb{Z}_2$ on-site symmetry is studied in detail.