On the probability of ferromagnetic strings in antiferromagnetic spin chains

TL;DR

This paper investigates the probability of forming ferromagnetic strings in antiferromagnetic spin chains using bosonization, revealing Gaussian and exponential decay behaviors at different temperatures and string lengths.

Contribution

It introduces a bosonization-based approach to analyze ferromagnetic string probabilities in the XXZ chain, including effects of temperature and magnetic field.

Findings

Probability is Gaussian at zero temperature.

Crossover to exponential decay at finite low temperatures.

Qualitative agreement with known numerical and exact results.

Abstract

We study the probability of formation of ferromagnetic string in the antiferromagnetic spin-1/2 XXZ chain. We show that in the limit of long strings with weak magnetization per site the bosonization technique can be used to address the problem. At zero temperature the obtained probability is Gaussian as a function of the length of the string. At finite but low temperature there is a crossover from the Gaussian behavior at intermediate lengths of strings to the exponential decay for very long strings. Although the weak magnetization per site is a necessary small parameter justifying our results, the extrapolation of obtained results to the case of maximally ferromagnetic strings is in qualitative agreement with known numerics and exact results. The effect of an external magnetic field on the probability of formation of ferromagnetic strings is also studied.