Exact Ground State Energy of Hubbard Rings in the Atomic Limit

TL;DR

This paper derives a simple analytic formula for the ground state energy of one-dimensional Hubbard rings in the atomic limit, valid for any number of sites and electrons, and explores ground state degeneracy and spin properties.

Contribution

It extends Lieb and Wu's analysis to provide a universal analytic expression for Hubbard rings in the atomic limit, including insights into degeneracy and spin.

Findings

Analytic ground state energy formula valid for all L and N

Insights into degeneracy and spin properties in the atomic limit

Numerical results illustrating the approach to the atomic limit

Abstract

Using a straightforward extension of the analysis of Lieb and Wu, we derive a simple analytic form for the ground state energy of a one-dimensional Hubbard ring in the atomic limit. This result is valid for an \textit{arbitrary} number of lattice sites $L$ and electrons $N \leq L$. Furthermore, our analysis, including an application of the theory of stochastic matrices, provides insight into the degeneracy and spin properties of the ground states in the atomic limit. We give numerical results which illustrate how the atomic limit is approached.