Dynamics of fractionalized mean-field theories: consequences for Kitaev materials

TL;DR

This paper advances the understanding of Kitaev materials by extending Majorana mean-field theory to include quantum phase information, enabling accurate dynamical correlator calculations and insights into material proximity to the Kitaev phase.

Contribution

It introduces a generalized Majorana mean-field approach that incorporates quantum phase information, improving the analysis of dynamical properties in Kitaev-like systems.

Findings

Small perturbations do not significantly change the dynamical correlator results.

$ ext{α-RuCl}_3$ may be farther from the Kitaev phase than previously believed.

The method reproduces exact results for the unperturbed model.

Abstract

There have been substantial recent efforts, both experimentally and theoretically, to find a material realization of the Kitaev spin-liquid--the ground state of the exactly solvable Kitaev model on the honeycomb lattice. Candidate materials are now plentiful, but the presence of non-Kitaev terms makes comparison between theory and experiment challenging. We rederive time-dependent Majorana mean-field theory and extend it to include quantum phase information, allowing the direct computation of the experimentally relevant dynamical spin-spin correlator, which reproduces exact results for the unperturbed model. In contrast to previous work, we find that small perturbations do not substantially alter the exact result, implying that $\alpha$-RuCl${}_3$ is perhaps farther from the Kitaev phase than originally thought. Our approach generalizes to any correlator and to any model where Majorana mean-field theory is a valid starting point.