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

2019/04/23 by Luana N. O. Vilela, LUCAS NASCIMENTO VILELA, K. Capelle +5 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Coulomb #Electron #Energy (signal processing) #Geometry #Ground state #Hubbard model #Mathematical physics #Mathematics #Monte Carlo method #Nonlinear system #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Statistical physics #Statistics #cond-mat.str-el

paper · pdf · doi:10.1088/1361-648x/ab32ac

published in Journal of Physics Condensed Matter 31(45), 455601 (IOP Publishing)

arxiv created 2019/04/23 · openalex publication_date 2019/07/17 · arxiv updated 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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