Twisted Injectivity in PEPS and the Classification of Quantum Phases

TL;DR

This paper introduces a new class of PEPS based on twisted group symmetries, providing a framework to classify 2D gapped quantum phases and connect them to Dijkgraaf-Witten TQFT.

Contribution

It develops a novel standard form for PEPS incorporating twisted symmetries, linking topological order to Dijkgraaf-Witten TQFT.

Findings

Constructed gapped, frustration-free Hamiltonians from twisted PEPS

Classified 2D quantum phases via the new PEPS standard form

Connected topological order to Dijkgraaf-Witten TQFT

Abstract

We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians which are gapped, frustration-free and include fixed points of the renormalization group flow. Moreover, we advance the classification of 2D gapped quantum spin systems by showing how this new standard form for PEPS determines the emergent topological order of these local Hamiltonians. Specifically, we identify their universality class as Dijkgraaf-Witten topological quantum field theory (TQFT).