Improved chain mean-field theory for quasi-one-dimensional quantum magnets

Abstract

A mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the nearest-neighbor chains as well as those in each chain are taken into account exactly. The self-consistent equation for the critical temperature contains the boundary-field magnetic susceptibilities of a multichain cluster, which can be evaluated accurately by some analytic or numerical methods, such as the powerful quantum Monte Carlo method. We show that the accuracy of the critical temperature of Q1D magnets as a function of the strength of interchain coupling is significantly improved compared with the conventional chain mean-field theory. It is also demonstrated that our approximation can predict nontrivial dependence of critical temperature on the sign (i.e., ferromagnetic or antiferromagnetic) of interchain coupling as well as on the impurity concentration in randomly diluted Q1D Heisenberg antiferromagnets.