Spinons, Solitons and Magnons in One-dimensional Heisenberg-Ising Antiferromagnets

TL;DR

This paper investigates the excitation spectra of one-dimensional Heisenberg-Ising antiferromagnets across different spin values, revealing phase transitions and quantum renormalization effects through series expansions and comparisons with known solutions.

Contribution

It provides a detailed calculation of excitation spectra for various spins in 1D Heisenberg-Ising antiferromagnets, including the transition to the Haldane phase and quantum renormalization effects.

Findings

Agreement of spinon-spectra with Johnson and McCoy for S=1/2

Gapless solitons indicating Haldane phase for S=1

Quantum renormalization factor of approximately 1.16 for S=3/2

Abstract

We calculate the excitation spectra for the one-$d$ Heisenberg-Ising antiferromagnets by expansions around the Ising limit. For $S=1/2$, the calculated expansion coefficients for the spinon-spectra agree term by term with the solution of Johnson and McCoy. For $S=1$, the solitons become gapless before the Heisenberg limit is reached, signalling a transition to the Haldane phase. By applying a staggered field we calculate the one-magnon spectra for the $S=1$ Heisenberg chain. For $S=3/2$ the quantum renormalization of the spin-wave spectra is calculated to be approximately $1.16$.