Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions

TL;DR

This paper introduces a new mean-field theory for quantum spin-1/2 Heisenberg antiferromagnets in 1D and 2D, accurately capturing quantum fluctuations and avoiding unphysical phase transitions.

Contribution

The authors develop a Hartree-Fock based mean-field approach that aligns with the Mermin-Wagner theorem and reproduces key quantum fluctuation effects in low-dimensional antiferromagnets.

Findings

Accurately reproduces Bethe ansatz results for 1D correlations

Avoids unphysical finite-temperature phase transitions

Provides reasonable heat capacity estimates across temperatures

Abstract

We construct a new mean-field theory for quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition in accord with Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.