Topological order in PEPS: Transfer operator and boundary Hamiltonians

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.

4+2 pages, 4+1 figures. v2: Major improvements and additions, with the focus shifted towards the transfer operator. Paper largely rewritten and significantly extended, title changed. v3: Minor changes, accepted version, Journal-Ref added