Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

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 ≈ 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 the S = 2 chain which has a gap Δ, the correlation length and the uniform susceptibility in the temperature range Δ < T < J are well predicted by the semi-classical theory of Damle and Sachdev.