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 S0ex0ex=0ex0ex1/2 Heisenberg chains. The environment of a chain C₀ is modeled by a number of neighboring chains C_δ, δ0ex0ex=0ex0ex±1,,±n, with the edge chains C_±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 α behaves as M~√α enhanced by a multiplicative logarithmic correction.