Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS

TL;DR

This paper demonstrates how tensor network methods can realize and manipulate anyon-permuting symmetries in topological phases, enabling the creation of domain walls, symmetry twists, and defect lines in PEPS models.

Contribution

It introduces a tensor network framework for implementing all unitary topological symmetries as MPOs in PEPS, including domain walls and defects.

Findings

MPOs realize all unitary topological symmetries in toric and color codes.

Domain walls enact symmetry transformations on anyons.

Open boundary conditions allow for symmetry twists and defect lines.

Abstract

We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all unitary topological symmetries for the toric and color codes. These operators act as domain walls that enact the symmetry transformation on anyons as they cross. By considering open boundary conditions for these domain wall MPOs, we show how to introduce symmetry twists and defect lines into the state.