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Chinese Physics Letters

Antiferromagnetic Phase Transition in the Quasi-Two-Dimensional Hubbard Model at Half Filling

Liu Qin-Yong, Tian Guang-Shan, Xin-Zhong Yan

Published May 1, 2004• 3 citations
Publisher

Abstract

We study the antiferromagnetic phase transition in the quasi-two-dimensional Hubbard model at half filling for a wide range of the Coulomb interaction U . By using the fluctuation-exchange approximation, we calculate the Néel transition temperature of the system as a function of the Coulomb interaction U . For weak-to-intermediate Coulomb interactions, the present calculation provides a reasonable result for the Néel temperature.

DOI
10.1088/0256-307x/21/5/049

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We study the antiferromagnetic phase transition in the quasi-two-dimensional Hubbard model at half filling for a wide range of the Coulomb interaction U . By using the fluctuation-exchange approximation, we calculate the Néel transition temperature of the system as a function of the Coulomb interaction U . For weak-to-intermediate Coulomb interactions, the present calculation provides a reasonable result for the Néel temperature.
The antiferromagnetic Ne\'el temperature TN{T}_{N}TN​ 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 43{4}^{3}43--103{10}^{3}103 sites, and used to determine TN{T}_{N}TN​. The size dependence of the results suggests that the transition is weakly first order at small to intermediate values of U.
We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott-Heisenberg antiferromagnet. At finite temperature, we find a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling.
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.
We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small UUU are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.