Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models

TL;DR

This study maps the phase diagram of spin-$S$ Kitaev-Heisenberg models, revealing that quantum spin liquid phases diminish rapidly with increasing spin, guiding future material searches.

Contribution

Extended the pseudofermion functional renormalization group method to analyze higher-$S$ Kitaev-Heisenberg models, systematically clarifying the stability of QSL phases across different spins.

Findings

QSL phases exist near pure Kitaev points for higher $S$

QSL phases shrink rapidly as $S$ increases, nearly vanishing for $S \\geq 2$

Phase boundaries between magnetic orders remain stable with increasing $S$

Abstract

The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-$S$ Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general $S$. We show that, similar to the $S=1/2$ case, the phase diagram for higher $S$ contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing $S$, becoming vanishingly narrow for $S\geq 2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search of higher-$S$ Kitaev materials.