Renormalization group analysis for bosonization coefficients in half-odd-integer Kitaev spin chains

TL;DR

This paper uses renormalization group analysis to study bosonization coefficients in half-odd-integer Kitaev spin chains, revealing scaling behaviors and symmetry properties relevant for understanding magnetic order.

Contribution

It provides a detailed RG analysis of bosonization formulas in specific Kitaev spin chains, identifying key coefficients and their dependence on model parameters.

Findings

Effects of symmetry breaking scale as 1/S in large-S limit.

Ten independent bosonization coefficients identified, five independent of Heisenberg coupling.

Qualitative agreement with DMRG numerical results.

Abstract

Based on a renormalization group (RG) analysis, we study the bosonization formulas in spin-$S$ Kitaev-Gamma and Kitaev-Heisenberg-Gamma chains in the $(K<0,\Gamma>0,J>0)$ parameter region, where $S$ is a half-odd integer. We find that the effects associated with the breaking of emergent continuous symmetries in bosonization formulas scale as $1/S$ in the large-$S$ limit, which is in qualitative agreement with DMRG numerical results for Kitaev-Gamma chains. In Kitaev-Heisenberg-Gamma chains, symmetry analysis reveals ten independent bosonization coefficients, five of which are predicted by the RG analysis to have no dependence on the Heisenberg coupling up to linear order. Our work may offer valuable input for determining magnetic ordering tendencies in two-dimensional Kitaev spin models within a quasi-one-dimensional approach.