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

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.

arXiv comment5 pages, 2 figures

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Cited by in corpus (6)

• Exact renormalization group for quantum spin systems
• Specific Heat Study of 1D and 2D Excitations in the Layered Frustrated Quantum Antiferromagnets Cs${}_2$CuCl${}_{4-x}$Br${}_x$
• Ground state selection by magnon interactions in the fcc antiferromagnet
• Spectral characteristics of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• Magneto-structural properties of the layered quasi-2D triangular-lattice antiferromagnets Cs${}_2$CuCl${}_{4-x}$Br${}_x$ for $x$ = 0,1,2 and 4
• Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D Regime