Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids

TL;DR

This paper provides an exact analytical approach to the S=3/2 Kitaev honeycomb model, revealing a rich phase diagram of gapped and gapless quantum spin liquids, and explores effects of anisotropy and emergent chiral phases.

Contribution

It introduces an SO(6) Majorana representation for spin 3/2, enabling exact flux representation and a quantitative mean-field analysis of the phase diagram.

Findings

Identification of gapped and gapless quantum spin liquids

Agreement between mean-field theory and numerical simulations

Connection between S=3/2 and S=1/2 Kitaev models via anisotropy

Abstract

The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z$_2$ gauge field. Employing an SO(6) Majorana representation of spin 3/2's, we find an exact representation of the conserved plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a $[001]$ single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak $[111]$ SIA, we discuss an emergent chiral QSL within a perturbation theory.