Exact Ground State Energy of Hubbard Rings in the Atomic Limit

Details Exact Ground State Energy of Hubbard Rings in the Atomic Limit Exact Ground State Energy of Hubbard Rings in the Atomic Limit

2008-06-10

arxiv.org/abs/0806.1761v4

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 10 figure files for 6 figures

Scientific paper

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.

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