Bosonic representation of spin operators in the field-induced critical phase of spin-1 Haldane chains

TL;DR

This paper develops a bosonized-field-theory representation for spin operators in the field-induced critical phase of spin-1 Haldane chains, enabling detailed analysis of correlation functions and perturbation effects.

Contribution

It introduces a comprehensive bosonization framework combining non-Abelian and Abelian methods for spin-1 Haldane chains in a critical phase, including effects of various perturbations.

Findings

Explicit asymptotic spin correlation functions derived.

Analysis of perturbation effects on the TLL state.

Insights into symmetry operations in the low-energy theory.

Abstract

A bosonized-field-theory representation of spin operators in the uniform-field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1 Haldane chains is formulated by means of the non-Abelian (Tsvelik's Majorana fermion theory) and the Abelian bosonizations and Furusaki-Zhang technique [Phys. Rev. B {\bf 60}, 1175 (1999)]. It contains massive magnon fields as well as massless boson fields. From it, asymptotic forms of spin correlation functions in the TLL phase are completely determined. Applying the formula, we further discuss effects of perturbations (bond alternation, single-ion anisotropy terms, staggered fields, etc) for the TLL state, and the string order parameter. Throughout the paper, we often consider in some detail how the symmetry operations of the Haldane chains are translated in the low-energy effective theory.