Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity

TL;DR

This paper introduces a simple analytical parametrization for the ground-state energy of the 1D Hubbard model that accurately incorporates Mott physics, spin effects, and inhomogeneity, outperforming previous models in accuracy and computational efficiency.

Contribution

The authors develop a new, more accurate analytical parametrization of the Hubbard model's ground-state energy, including extensions to spin-dependent and inhomogeneous systems, validated against numerical data.

Findings

Improved agreement with Bethe-Ansatz data

Correct prediction of positive Mott gap at half filling

Effective extension to inhomogeneous systems

Abstract

Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The resulting parametrization is shown to be in better agreement with highly precise data obtained from fully numerical solution of the Bethe-Ansatz equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402 (2003)]. Unlike these earlier proposals, the present parametrization correctly predicts a positive Mott gap at half filling for any U>0. The construction is extended to spin-dependent phenomena by parametrizing the magnetization-dependence of the ground-state energy using further exact results and numerical benchmarking. Lastly, the parametrizations developed for the spatially uniform model are extended by means of a simple local-density-type approximation to spatially inhomogeneous models, e.g., in the presence of impurities, external fields or trapping potentials. Results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost.