Topological order in PEPS: Transfer operator and boundary Hamiltonians

TL;DR

This paper investigates topological phases in PEPS by analyzing the transfer operator and boundary Hamiltonians, revealing universal non-local features and local symmetry properties that characterize topological order and edge modes.

Contribution

It introduces a method to identify topological order from the PEPS transfer operator and analyzes the boundary Hamiltonian structure, linking entanglement properties to topological features.

Findings

Topological order can be detected from the PEPS transfer operator.

Boundary Hamiltonian has a universal non-local part and a local symmetry-inherited part.

The structure of the boundary Hamiltonian reflects the nature of topological phases.

Abstract

We study the structure of topological phases and their boundaries in the Projected Entangled Pair States (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator, and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal non-local part which encodes the nature of the topological phase, and a non-universal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes.