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Metal-insulator transition in the generalized Hubbard model

Anatoly A. Ovchinnikov

Published Jan 1, 1994• 7 citations
OpenAlex

Abstract

We present the exact ground-state wave function and energy of the generalized Hubbard model, subjected to the condition that the number of double occupied sites is conserved, for a wide, physically relevant range of parameters. For one hole and one double occupied site the existence of the ferromagnetic ground-state is proved which allow 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. 1

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We present the exact ground-state wave function and energy of the generalized Hubbard model, subjected to the condition that the number of double occupied sites is conserved, for a wide, physically relevant range of parameters. For one hole and one double occupied site the existence of the ferromagnetic ground-state is proved which allow 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. 1
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.
We study a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and general correlated hopping under the condition that the number of doubly occupied sites is conserved. We find the exact ground state (GS) in arbitrary dimension in two wide regions of parameters. In one of them the GS is a Mott insulator (MI) and in the other it is a charge-density wave (CDW). The boundary of the MI and a large part of that of the CDW are determined exactly for relevant lattices. We study numerically the effect of relaxing the above-mentioned condition.
We study the metal-insulator transition of the d-dimensional Hubbard model by treating the hopping term between adjacent 1-d chains in the frame of a Clifford linearization scheme, and keeping the full model along the chains. A general equation for the critical point is worked out in terms of the correlation functions of the one-dimensional model, assuming that the transition is of the second order. The equation, which holds at any temperature, is here investigated especially at T=0, where the latter condition holds true. The solution shows the existence of an insulating ground state in any d only at half-filling for U strictly positive, as in the exact 1-d case. The transition is found to be related to a parameter reminiscent of entropy.