Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model

TL;DR

This paper develops a Schwinger boson mean field theory for the integer-spin Heisenberg-Kitaev model, identifying a chiral quantum spin liquid state that matches numerical data and could be realized in specific materials.

Contribution

It introduces a mixed singlet and triplet pairing Schwinger boson approach that accurately describes competing quantum spin liquids, including a chiral state consistent with numerical results.

Findings

Identification of a chiral quantum spin liquid state matching exact diagonalization data.

The chiral spin liquid survives up to large spin S ≈ 2.

Proposed candidate materials for realizing the spin liquid state.

Abstract

Motivated by the possibility of finding a bosonic quantum spin liquid in the integer spin-$S$ Heisenberg-Kitaev model on the honeycomb lattice, we derive a Schwinger boson mean field theory involving both singlet and triplet pairing channels which includes hopping and pairing operators on equal footing. The mixed construction introduced here is justified by the good comparison with exact diagonalization energies of the $S \leq 3/2$ Heisenberg-Kitaev model and the perfect match with the Luttinger-Tisza semiclassical energies obtained at large-$S$. We find various competing gapped quantum spin liquids close to the Kitaev point. A comparison of their spin excitation spectrum with the dynamical structure factor obtained from exact diagonalizations allows us to identify the physical spin liquid {\it Ansatz} of the model. In particular, we identify a chiral quantum spin liquid state whose spin excitation spectrum follows closely the exact diagonalization data and survives up to large spin $S \lesssim 2$. We propose this state as a promising quantum spin liquid candidate for the integer spin-$S$ antiferromagnetic Kitaev model which may be realized in $S=1$ Kitaev materials A$_3$Ni$_2$XO$_6$ and KNiAsO$_4$.