Strongly correlated electrons in fcc lattices

Abstract

The Hubbard model was created in 1963 to study the properties of electron correlations in narrow energy bands. The intention was to model the properties of 3d transition metals. Since then, several new applications have been developed for the model. However, because of theoretical difficulties in the obtainment of its properties in three-dimensional lattices the modeling of 3d transition metals continues as a theoretical important challenge. In this work, using a grand canonical quantum Monte-Carlo method we performed an exhaustive study of the average energy ( E) as a function of the number of particles per site ( n) and of the dependence of n with the temperature ( T) for fcc lattices. We find that, for all temperatures, when the relative magnitude of the Coulombian repulsion to transfer integral ( U/ t) is of the order of 2, E has a minimum for n around 0.6. Thus, as n∼0.6 and U/ t∼2 are the known values in the literature for nickel, we show the natural applicability of a single-band model in the study of the properties of nickel.