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arXiv:cond-mat/0303501

From Hubbard model to t-J-U model: a canonical transformation formalism, the metal-insulator transition and mean-field state

Yue Yu

Published Mar 24, 2003• 0 citations
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Abstract

We prove that the t-J-U model can be deduced from the Hubbard model at a large but finite U by a canonical transformation. We argue that the system may have a metal-insulator transition at a critical on-site Coulomb interaction whose value, however, is smaller than that in previous calculations in which the kinetic energy has a double counting. In a mean field theory and a special choice of the parameters, we show that the metallic state may be equivalent to the gossamer superconducting state proposed by Laughlin recently.

DOI
10.48550/arxiv.cond-mat/0303501

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Recently a new phenomenological Hamiltonian was proposed to describe the superconducting cuprates in which correlations and on-site Coulomb repulsion are introduced by partial Gutzwiller projection. This Gossamer Hamiltonian has an exact ground state and differs from the t-J and Hubbard Hamiltonians in possessing a powerful attractive interaction among electrons responsible for Cooper pairing in the d-wave channel. It is a faithful description for a superconductor with strong on-site electronic repulsion. The superconducting tunneling gap remains intact and despite on-site repulsion. Near half-filling the Gossamer superconductor with strong repulsion has suppressed photoemission intensities and superfluid density, is unstable toward an antiferromagnetic insulator and possesses an incipient Mott-Hubbard gap. The Gossamer technique can be applied to metallic ground states thus possibly serving as an apt description of strongly correlated metals. Such a Gossamer metallic phase, just as the Gossamer superconducting one, becomes arbitrarily hard to differentiate from an insulator as one turns the Coulomb correlations up near half-filling. Both the metallic and superconducting states undergo a quantum phase transition to an antiferromagnetic insulator as one increases the on-site Coulomb repulsion. In the Gossamer model we reach the critical point at half-filling by fully projecting out the double occupancy. Such a critical point might be the Anderson Resonating Valence bond state.
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We present the exact ground-state wave function and energy of the generalized Hubbard model, subject to the condition that the number of doubly occupied sites is conserved. For a wide, physically relevant range of parameters. For one hole and one doubly occupied site the existence of the ferromagnetic ground state is proved which allows one to determine the critical value of the on-site repulsion corresponding to the point of metal-insulator transition. For the one-dimensional model the exact solution for special values of the parameters is obtained.