D--dimensional half--filled Hubbard model. Zero temperature paramagnetic solution

TL;DR

This study explores how lattice dimension influences the properties of the half-filled paramagnetic Hubbard model at zero temperature, analyzing key electronic characteristics across one, two, and three dimensions.

Contribution

It introduces a method to treat lattice dimension as an external parameter in the Hubbard model, enabling analysis of dimensional effects on electronic properties.

Findings

Number of doubly occupied sites varies with dimension

Electronic density of states depends on lattice dimension

Momentum distribution shows dimension-dependent features

Abstract

In this paper we investigate effects of a lattice dimension on strongly correlated electronic systems at $T=0 K$. The model for numerical calculations is formalized in terms of the integral equations which were obtained previously for the half -- filled paramagnetic Hubbard model. The assumption that all relevant functions of the system have a magnitude dependence of momentus vectors makes ultimately possible treating a lattice dimension $D$ as an external parameter. We here submit for consideration the number of doubly occupied lattice sites, the electronic density of states, and the momentum distribution in electronic occupation numbers at $D$=1, $D$=2, $D$=3