Monte Carlo Study of Correlations in Quantum Spin Ladders

We study antiferromagnetic spin-½ Heisenberg ladders, comprised of $n_c$ chains ($2\le n_c\le 6$) with ratio $\frac{J_{\perp }}{J_{\parallel }}$ of inter-chain to intra-chain couplings. The correlation length $\xi \mathrm{}\left(T\right)\mathrm{}$ is deduced from measurements of the correlation function. For even $n_c$, the static structure factor exhibits a peak at a temperature below the corresponding spin gap. Results for isotropically coupled ladders ($\frac{J_{\perp }}{J_{\parallel }}=1\mathrm{}$) are compared to those for the single chain and the square lattice. For $\frac{J_{\perp }}{J_{\parallel }}\le 0.5$, the correlation function of the two-chain ladder is in excellent agreement with analytic results from conformal field theory, and $\xi \mathrm{}\left(T\right)\mathrm{}$ exhibits simple scaling behavior.