# Approximate expression for the ground-state energy of the two- and three-dimensional Hubbard model at arbitrary filling obtained from dimensional scaling

## TL;DR

This paper introduces a nonlinear dimensional scaling method to accurately approximate the ground-state energy of the Hubbard model in 2D and 3D, extending the applicability beyond existing QMC data.

## Contribution

The authors develop a nonlinear scaling relation based on linear discrete dimensional scaling, providing accurate ground-state energy estimates for the Hubbard model at arbitrary fillings.

## Key findings

- Accurate approximations of ground-state energy in 2D and 3D Hubbard models.
- Predictions made for parameter regimes lacking QMC data.
- Validation against auxiliary-field quantum Monte Carlo results.

## Abstract

We generalize the linear discrete dimensional scaling approach for the repulsive Hubbard model to obtain a nonlinear scaling relation that yields accurate approximations to the ground-state energy in both two and three dimensions, as judged by comparison to auxiliary-field quantum Monte Carlo (QMC) data. Predictions are made for the per-site ground-state energies in two and three dimensions for $n$ (filling factor) and $U$ (Coulomb interaction) values for which QMC data are currently unavailable.