Projective symmetry of partons in Kitaev's honeycomb model

TL;DR

This paper investigates how the gauge field in Kitaev's honeycomb model causes partons to exhibit projective symmetries, affecting their spectral degeneracies and revealing a double cover of the point group symmetry.

Contribution

It demonstrates that the gauge field induces projective symmetry in the parton spectrum, specifically showing that the ground state symmetry is a double cover of the physical point group.

Findings

Partons have half-integer orbital angular momenta due to gauge fields.

Spectral multiplicities reflect projective symmetries, not just point-group symmetries.

The ground state symmetry group is the double cover of the point group.

Abstract

Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of Kitaev's honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities reflect not the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.