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Communications in Theoretical Physics

The Groundstate of 2-Dimensional Infinite- U Hubbard Model with a Single Hole

Z. Song, Zhenqing Yang, Guo-Zhu He

Published Mar 1, 1993• 0 citations
Publisher

Abstract

The groundstate energies of 1- and 2-D infinite- U Hubbard models with a single hole are obtained by a simple method. It is found that the groundstates for an arbitrary finite system are multiple degenerate states with even is the number of sites). Based on these results, it is shown that the hole and the spin-flip(s) can not form a bound state, then it provides an alternate proof of Nagaoka's theorem.

DOI
10.1088/0253-6102/19/2/243

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Modern Physics Letters B•Oct 30, 1993•0 citations
The groundstate energies of 1- and 2-D infinite- U Hubbard models with a single hole are obtained by a simple method. It is found that the groundstates for an arbitrary finite system are multiple degenerate states with even is the number of sites). Based on these results, it is shown that the hole and the spin-flip(s) can not form a bound state, then it provides an alternate proof of Nagaoka's theorem.
The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.
In this paper, we have rigorously shown that, in a thermodynamic limit, there always exists a one-spin-flipped state degenerate with the Nagaoka state in one-band Hubbard model on a two and three-dimensional simple cubic lattice when the number of holes [Formula: see text] (with 0≤α<1, N∧ and N e are the numbers of sites and electrons respectively) for all U (including U=∞). It is also shown that there does not exist a finite critical value U c for which, when U>U c , the Nagaoka state has the ground-state energy of the system for a two-dimensional square lattice when ρ→0.