Universal diffusive decay of correlations in gapped one-dimensional systems

TL;DR

This paper demonstrates that a semiclassical approach reveals a universal diffusive decay pattern in finite temperature correlations across various gapped one-dimensional quantum spin models, including experimental relevance.

Contribution

It extends a semiclassical method to analyze finite temperature correlations in multiple 1D gapped spin models, showing universality in their decay behavior.

Findings

Universal diffusive decay in correlation functions

Applicability to S=1 antiferromagnetic Heisenberg chain

Generalization to O(N) and sine-Gordon models

Abstract

We apply a semiclassical approach to express finite temperature dynamical correlation functions of gapped spin models analytically. We show that the approach of [A. Rapp, G. Zarand, Phys. Rev. B 74, 014433 (2006)] can also be used for the S=1 antiferromagnetic Heisenberg chain, whose lineshape can be measured experimentally. We generalize our calculations to O(N) quantum spin models and the sine-Gordon model in one dimension, and show that in all these models, the finite temperature decay of certain correlation functions is characterized by the same universal semiclassical relaxation function.