Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems

A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled $S=1\mathrm{}/2$ Heisenberg chains. The environment of a chain $C_0$ is modeled by a number of neighboring chains $C_{\delta }$, $\delta =\pm 1,\dots ,\pm n$, with the edge chains $C_{\pm n}$ coupled to a staggered field. Using a quantum Monte Carlo method, the effective $(2n+1)$-chain Hamiltonian is solved self-consistently for $n$ up to $4$. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization $M$ for small interchain couplings $\alpha$ behaves as $M\sim \sqrt{\alpha }$ enhanced by a multiplicative logarithmic correction.