Lattice-gas model driven by Hubbard electrons

Abstract

Self-consistent Monte Carlo simulations are undertaken for a lattice-gas model which is driven by the free energy of electrons described by a Hubbard model with electronic hopping restricted to ions at nearest-neighbor sites. Our previous work, an independent-electron tight-binding lattice-gas model (bcc or fcc), is modified to introduce two effects: the disorder of the dense system and, more importantly, the role of the electronic correlation. The first effect is achieved using an fcc lattice, but restricted so an occupied site can have no more than eight, instead of twelve, occupied nearest-neighbor sites. To treat correlations, the electronic intra-atomic repulsion is, at first, included via the Gutzwiller approximation at finite temperature; this approach is simple enough to be solved for all cases in the large, disordered systems used in our Monte Carlo simulations but can still give a good qualitative representation of the main effects of the electronic correlations. Then, the exact treatment of the Hubbard model for clusters with up to six atoms is integrated into the calculation. We obtain vapor-liquid coexistence curves and then, approximations to the electronic conductivities and paramagnetic susceptibilities at coexistence conditions. This simple model is, in part, motivated by experiments on the alkali-metal fluids.

Hard-sphere fluid with tight-binding electronic interactions: A glue model treatment

“…There is no doubt that further corrections to our model, for instance explicit consideration of Hubbard terms in the electronic Hamiltonian, would modify our results. But, first, such terms are unnecessary to keep the moderately low density system nonmetallic ͑with a conductivity which decreases as the density is lowered͒ and, second, preliminary data, along with our previous experience, 5 indicate that such modifications would not be qualitative. Therefore, it appears that indeed the metal to nonmetal transition in this system is dominantly due to correlations among the ionic positions which are induced by the electronic energy.…”

“…4 Then, the effects of a Hubbard interaction among electrons was considered. 5 That work was recently reviewed. 6 In this paper, our previous work is generalized, removing previous restrictions, by allowing a continuum of ionic positions, only limited by hard-sphere interactions, and using an electronic hopping with an exponential dependence on the hopping distance.…”

Effects of electron correlation on thermodynamic properties of expanded alkali fluids

“…Among the approximations in this theory, the importance of improving the mean-field approximation for atomic arrangements has been pointed out by Reinald-Falagán et al [11,12]. They concluded that it is important to treat the local atomic configuration beyond the mean-field approximation self-consistently with the electronic energy to reproduce the asymmetric feature of the LV coexistence curve.…”

“…the curve describing the boundary of the coexisting liquid and vapour phases on the volume versus temperature plane, is strongly asymmetric and the law of the rectilinear diameter breaks down over a large temperature range for fluid alkalis such as Rb and Cs. Among recent theoretical research in relation to the above experimental results, the work most relevant to the present paper is that by Reinaldo-Falagán et al [11,12]. In the earlier paper [11], using a model which is the single-particle version of the latticegas Hubbard model presented above, and a self-consistent method for determining the ionic configurations and the electronic energies, they obtained results for the thermodynamic and electronic properties of expanded alkali fluids which agree qualitatively with the experimental results.…”

“…In particular, they concluded that the extreme asymmetry of the coexistence curves is reproduced by taking account self-consistently of the effect of the local coordination in determining the free energy per ion. Most recently [12], they modified their previous work to include the effects of electron correlation. Their theory is an extension of the work by Nara et al; they employed the Gutzwiller approximation for the lattice-gas Hubbard model at finite temperatures and determined the electronic and atomic distributions self-consistently as in their previous work.…”