Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid

TL;DR

This paper introduces a simple scaling hypothesis to estimate the ground-state energy of large systems like the Hubbard model and Fermi liquid from smaller building blocks, achieving accurate results across different dimensions and interaction strengths.

Contribution

The paper proposes a physically motivated scaling approach that accurately estimates large system energies from smaller components, validated on the Hubbard model and electron liquid.

Findings

Accurately estimates 1D Hubbard energy from a 2-site dimer.

Recovers exact limits for U→0 and U→∞ in higher dimensions.

Close agreement with Quantum Monte Carlo data for intermediate U.

Abstract

A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is illustrated for the electron liquid, and the Hubbard model. By means of this scaling argument the energy of the one-dimensional half-filled Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining quantitative agreement with the exact one-dimensional Bethe-Ansatz solution, and the energies of the two- and three-dimensional half-filled Hubbard models are estimated from the one-dimensional energy, recovering exact results for $U\to 0$ and $U\to \infty $ and coming close to Quantum Monte Carlo data for intermediate $U$.