Interaction energy functional for lattice density functional theory: Applications to one-, two- and three-dimensional Hubbard models

TL;DR

This paper introduces a new interaction-energy functional for lattice density functional theory, improving the description of electron correlations in Hubbard models across different dimensions, with applications to ground-state and excitation properties.

Contribution

A novel approximation for the interaction-energy functional in lattice DFT that accurately captures strong correlations and crossover behavior in Hubbard models.

Findings

Accurate ground-state energies across dimensions

Improved charge-excitation gap predictions

Enhanced charge susceptibility calculations

Abstract

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\gamma]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of $W$ is obtained throughout the domain of representability of $\gamma_{ij}$, including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for $W$. Goals and limitations of the different approximations are discussed.