Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems

TL;DR

This paper develops a multi-chain mean-field theory for weakly coupled S=1/2 Heisenberg chains, using quantum Monte Carlo to analyze the magnetization behavior and compare with large lattice simulations.

Contribution

It introduces a multi-chain mean-field approach combined with quantum Monte Carlo for quasi-1D quantum spin systems, providing new insights into their magnetic properties.

Findings

Magnetization scales as alpha^{1/2} with a logarithmic correction.

Theoretical results agree with large-scale simulations.

Method extends to systems with multiple coupled chains.

Abstract

A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge chains (d=+/-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=A*alpha^1/2 enhanced by a multiplicative logarithmic correction.