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Journal of Physics A Mathematical and General

The binding energy and the charged gaps in the negative-UHubbard model: some rigorous results

Guang-Shan Tian

Published Aug 7, 1997• 8 citations
Publisher

Abstract

By applying Lieb's spin-reflection-positivity method and exploiting a commutation relation satisfied by the negative-U Hubbard Hamiltonian, we prove two rigorous theorems on the binding energy of fermions, the one-particle and the two-particle gaps for the model on an arbitrary finite lattice.
DOI
10.1088/0305-4470/30/15/019

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In this paper, by applying a simplified version of Lieb's spin-reflection-positivity method, which was recently developed by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some general properties of the boson-fermion Hamiltonian, which has been widely used as a phenomenological model to describe the real-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive coupling V, which represents the spontaneous decay and recombination process between boson and fermion in the model, the pairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermion Hamiltonian is always larger than its charged gap, as predicted by the pre-paired electron theory.
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