A Monte Carlo Study of Correlations in Quantum Spin Ladders

TL;DR

This study uses Monte Carlo simulations to analyze correlations in antiferromagnetic quantum spin ladders, revealing how correlation lengths and structure factors behave across different ladder configurations and coupling ratios.

Contribution

It provides detailed Monte Carlo results for spin--1/2 Heisenberg ladders with varying chain numbers and coupling ratios, comparing them to theoretical predictions and other lattice structures.

Findings

Correlation length $\xi(T)$ exhibits simple scaling for two-chain ladders at low coupling ratios.

Static structure factor peaks at temperatures below the spin gap for even-leg ladders.

Results align with conformal field theory for certain coupling regimes.

Abstract

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