Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid

TL;DR

This paper investigates how combined symmetries in PEPS influence the entanglement spectrum, providing insights into modeling chiral topological phases and resolving discrepancies with theoretical expectations.

Contribution

It analyzes the constraints imposed by multiple symmetries on PEPS tensors and applies the findings to a chiral spin liquid state, clarifying entanglement spectrum features.

Findings

Symmetry interplay affects entanglement spectrum structure.

Discrepancies with chiral conformal field theory are explained.

Additional $U(1)$ symmetry resolves spectrum discrepancies.

Abstract

Projected entangled pair states (PEPS) provide exact representations for many non-chiral topologically ordered states whereas their range of applicability to interacting chiral topological phases remains largely unsettled. In this context, the symmetries of the local PEPS tensors are crucial for determining the characteristic topological features of the state. In this article we examine the constraints that arise when different symmetries are imposed simultaneously on the local tensor such as internal $SU(2)$, point group and translation symmetry. We show how the interplay of these symmetries manifests in the entanglement spectrum which is the main diagnostic tool for chiral topological order. We apply our results to a spin liquid PEPS introduced previously as a chiral generalization of the resonating valence bond state. Our findings explain the discrepancies observed between the entanglement spectrum of this state and the expected edge spectrum described by a chiral conformal field theory. Finally, in a certain parameter region where this PEPS possesses an additional $U(1)$ symmetry we are able to resolve these discrepancies and obtain an entanglement spectrum with the expected state countings and conformal weight.