Density-Matrix functional theory of strongly-correlated lattice fermions

TL;DR

This paper develops a density functional theory for lattice fermions using the single-particle density matrix, providing accurate results for strongly correlated systems and extending to two dimensions.

Contribution

It introduces a new DFT approach based on the density matrix and derives an explicit approximation for the Hubbard model's interaction energy functional.

Findings

Excellent agreement with Bethe-Ansatz solutions in 1D

New results for ground-state energy in 2D

Effective description of strong correlations

Abstract

A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the Hubbard model is derived from exact dimer results, scaling properties of W[gamma] and known limits. Systematic tests on the one-dimensional chain show a remarkable agreement with theBethe-Ansatz exact solution for all interaction regimes and band fillings. New results are obtained for the ground-state energyand charge-excitation gap in two dimensions. A successful description of strong electron correlations within DFT is achieved.