Monte Carlo Study of Correlations in Quantum Spin Ladders

Abstract

We study antiferromagnetic spin-\textonehalf{} Heisenberg ladders, comprised of ${n}_{c}$ chains ($2\ensuremath{\le}{n}_{c}\ensuremath{\le}6$) with ratio $\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}$ of inter-chain to intra-chain couplings. The correlation length $\ensuremath{\xi}(T)$ 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 ($\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}=1$) are compared to those for the single chain and the square lattice. For $\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}\ensuremath{\le}0.5$, the correlation function of the two-chain ladder is in excellent agreement with analytic results from conformal field theory, and $\ensuremath{\xi}(T)$ exhibits simple scaling behavior.