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arXiv · 1802.07579

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

A. Werth·P. Kopietz·O. Tsyplyatyev
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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.

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A. Werth, P. Kopietz, O. Tsyplyatyev. 2018-02-21. Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions. https://doi.org/10.1103/physrevb.97.180403

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