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

TL;DR

This paper introduces an improved mean-field theory for quasi-one-dimensional quantum magnets that accurately predicts critical temperatures and their dependence on interchain coupling, magnetic interactions, and impurities.

Contribution

A new Bethe-type effective-field mean-field approach that incorporates quantum and thermal fluctuations for better accuracy in Q1D magnets.

Findings

Enhanced accuracy of critical temperature predictions.

Ability to model dependence on interchain coupling sign.

Predicts effects of impurities on critical temperature.

Abstract

A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our new 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 new 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.