Monte Carlo Study of Correlations in Quantum Spin Chains at Non-Zero Temperature

TL;DR

This study uses quantum Monte Carlo simulations to analyze correlations and susceptibilities in antiferromagnetic Heisenberg spin chains of various spins at low temperatures, confirming classical and semi-classical predictions.

Contribution

It provides a comprehensive numerical analysis of spin correlations in quantum chains across different spins and temperatures, extending understanding to low-temperature regimes.

Findings

High-temperature results match classical spin chain predictions.

Correlation length and susceptibility in S=2 chains align with semi-classical theory.

Numerical data down to T/J ≈ 0.01 enhances understanding of quantum spin chain behavior.

Abstract

Antiferromagnetic Heisenberg spin chains with various spin values ($S=1/2,1,3/2,2,5/2$) are studied numerically with the quantum Monte Carlo method. Effective spin $S$ chains are realized by ferromagnetically coupling $n=2S$ antiferromagnetic spin chains with $S=1/2$. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, $T/J \approx 0.01$. The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of $S$. For $S$=2 chains which have a gap $\Delta$, the correlation length and the uniform susceptibility in the temperature range $\Delta < T < J$ are well predicted by a semi-classical theory due to Damle and Sachdev.