Dynamics of a quantum spin liquid beyond integrability $-$ the Kitaev-Heisenberg-$\Gamma$ model in an augmented parton mean-field theory

TL;DR

This paper develops an augmented parton mean-field theory for the Kitaev-Heisenberg-$\Gamma$ model, accurately capturing the quantum spin liquid's dynamics and analyzing how integrability breaking affects spin correlations and experimental signatures.

Contribution

It introduces a controlled perturbation approach to study non-integrable effects in the Kitaev quantum spin liquid using an extended parton mean-field framework.

Findings

Broadening of the response peak with broken integrability

Generation of further-neighbor correlations

Loss of rotational symmetry in the structure factor

Abstract

We present an augmented parton mean-field theory which (i) reproduces the $exact$ ground state, spectrum, and dynamics of the quantum spin liquid phase of Kitaev's honeycomb model; and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the $K-J-\Gamma$ model which includes Heisenberg and symmetric-anisotropic (pseudo-dipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency; the generation of further-neighbour correlations and their structure in real- and spin-space; and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach, and also view the neutron scattering experiments on the putative proximate quantum spin liquid material, $\alpha$-RuCl$_3$, in the light of the results from this extended parton theory.