Systematic construction of density functionals based on matrix product state computations

TL;DR

This paper introduces a systematic method for constructing density functionals in density functional theory using matrix product state computations, enabling systematic improvements beyond local density approximations.

Contribution

The paper presents a new systematic approach to approximate density functionals, combining an efficient ansatz with a fitting strategy based on training densities from matrix product state calculations.

Findings

The method effectively approximates exchange-correlation energies.

Systematic improvements are achieved beyond local density approximation.

Approximations generalize well to different target densities.

Abstract

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz whose non-locality can be increased systematically. Second, we present a fitting strategy that is based on systematically increasing a reasonably chosen set of training densities. We investigate our procedure in the context of strongly correlated fermions on a one-dimensional lattice in which we compute accurate training densities with the help of matrix product states. Focusing on the exchange-correlation energy, we demonstrate how an efficient approximation can be found that includes and systematically improves beyond the local density approximation. Importantly, this systematic improvement is shown for target densities that are quite different from the training densities.