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Journal of Physics Condensed Matter

Re-entrant antiferromagnetism within a weak-coupling treatment of the Hubbard model

Einar Halvorsen, G. Czycholl

Published Nov 21, 1994• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/6/47/016

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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 study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and U.
We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.
We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.
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.
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to T=t20T=\frac{t}{20}T=20t​ (t=hoppingt=\mathrm{hopping}t=hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion UUU. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced