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physica status solidi (b)

Static approximation for the Hubbard model: Paramagnetic phase at finite temperatures

J. Mertsching

Published Feb 1, 1975• 4 citations
Publisher

Abstract

Abstract The static approximation for the Hubbard model by Puff and Weller [1] is discussed for finite temperatures. The distribution function of the stochastic site occupation numbers, the single‐particle density of states, and the free energy are calculated for temperatures much smaller than the bandwidth and the correlation energy.
DOI
10.1002/pssb.2220670226

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The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.
Abstract We study metal-insulator phase diagram in the half-filled disordered Hubbard model at finite temperature. We calculate the averaged local density of states at the Fermi level and the site occupation as a function of the on-site energy at finite temperature by using typical medium theory with an impurity solver of equation of motion method. Although the metallicity in the correlated metallic region changes with temperature change, the phase diagram is almost temperature independent. We find fairly good agreement between our site occupation and those obtained by the typical medium method with other impurity solver.
Abstract In a previous paper the Green function for the Hubbard model is represented by a functional average of the Green function for an electron moving in a local time dependent potential Uvi(t) taking only the values 0 and U. Here this functional average is calculated with an ad hoc assumed Poisson distribution governing the jumps of Uvi(t). In a single‐site approximation the Poisson average can be calculated exactly and leads to a self‐consistent ‚dynamic’︁ scheme interpolating between band and atomic limit. For a half‐filled band in the paramagnetic case at zero temperature for strong Coulomb repulsion U ≈ 2 two subbands are obtained separated by a minimum of the density of states.
High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.