Gapless edge states of BF field theory and translation-symmetric Z2 spin liquids

TL;DR

This paper investigates gapless edge states in translation-symmetric Z2 spin liquids, linking physical boundary phenomena to BF topological field theories and classifying these theories based on lattice symmetries.

Contribution

It introduces a series of mean-field models for Z2 spin liquids, connects their edge states to BF theories, and classifies BF theories according to lattice symmetries.

Findings

Gapless edge states arise from boundary Majorana fermions.

BF theories describe ground state degeneracies and crystal momenta.

A classification scheme for BF theories based on lattice symmetries.

Abstract

We study possible gapless edge states of translation-symmetric Z2 spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of Z2 spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these Z2 spin liquids and find their effective BF theory descriptions. The effective BF theories are shown to describe the crystal momenta of the ground states and their degeneracies and to predict the edge theories of these Z2 spin liquids. As a byproduct, we obtained a way to classify the BF theories reflecting the lattice symmetries. We discuss in closing three-dimensional Z2 spin liquids with gapless surface states on the cubic lattice.