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Physical review. B, Condensed matter

Phase diagram of the half-filled 3D Hubbard model

Richard T. Scalettar, Douglas J. Scalapino, Robert L. Sugar, D. Toussaint

Published Mar 1, 1989• 81 citations
Publisher

Abstract

The antiferromagnetic Ne\'el temperature ${T}_{N}$ is calculated as a function of the Coulomb interaction U for a half-filled 3D Hubbard model. Numerical results are given for the specific heat and staggered magnetic suspectibility on periodic lattices ranging from ${4}^{3}$--${10}^{3}$ sites, and used to determine ${T}_{N}$. The size dependence of the results suggests that the transition is weakly first order at small to intermediate values of U.

DOI
10.1103/physrevb.39.4711

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We have calculated the $U\ensuremath{-}T$ phase diagram of the half-filled simple-cubic Hubbard model (UUU: interaction, TTT: temperature) by making use of the two interpolation theories, the single-site spin-fluctuation (SSF) theory proposed by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) by Kakehashi and Fulde. The results are compared with those of the recent Monte Carlo (MC) calculations made by Hirsch for a three-dimensional 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 lattice. The N\'eel temperatures TN{T}_{N}TN​ calculated with the MC method are about 70% higher than those calculated with the mean-field-type theories of the SSF and VA though the UUU dependence of the amplitudes of the local moments and charge fluctuations agrees well with our results. This suggests an overestimation of TN{T}_{N}TN​ up to 100% in Hirsch's calculations, whose conceivable origins are discussed. We present also the result of the internal energy as a function of TTT and UUU calculated using the SSF and VA.
We study the infinite-dimensional Hubbard model within the self-consistent second-order U-perturbation treatment (SOPT), which is a conserving approximation and the simplest systematic improvement of the Hartree approximation (HA). For half filling we find antiferromagnetic solutions, but even for small Coulomb repulsion U the critical temperature is substantially reduced compared to that obtained in the HA. We construct the phase diagram as a function of doping and find regions of re-entrant behaviour in the temperature dependence of the staggered magnetization away from half filling. The stability of the ordered solutions is investigated by calculation of the grand canonical potential and the filling fraction dependence of the chemical potential; for small values of U the antiferromagnetic phase transition is continuous (as usual), but for larger U the SOPT yields a first-order phase transition. For low temperatures and away from half filling there may be a region of phase coexistence between the antiferromagnetic and homogeneous phases.