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International Journal of Modern Physics B

STUDY ON A TOY MODEL OF STRONGLY CORRELATED ELECTRONS

Flavio S. Nogueira, E. V. Anda

Published Dec 15, 1996• 20 citations
Publisher

Abstract

A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping an equivalence of the model with the Hubbard model with infinite range hopping is established. The generalization to the case with N components is made.

DOI
10.1142/s0217979296002014

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International Journal of Modern Physics B•Jan 1, 1991•287 citations
A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping an equivalence of the model with the Hubbard model with infinite range hopping is established. The generalization to the case with N components is made.
A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping is established the equivalence of the model with the Hubbard model with infinite range hopping. The generalization to the case with NNN components is made.
Starting from the exact solution of the Hubbard model in the atomic limit, and treating the hopping term as a perturbation by means of a diagram technique, we discuss the electronic structure of the model in some simple approximations. We show that a metal-insulator transition is obtained above a critical value of the on-site Coulomb interaction in a self-consistent evaluation of the one-particle Green's function to one-loop order. A relationship with results in infinite dimensions is briefly discussed.
A brief introduction to the bosonization method for interacting one-dimensional fermion systems is given. Using these results, the long-distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu. For infinite U the results are generalized to the case of nonzero nearest-neighbour interaction. The behaviour of thermodynamic quantities, of the frequency-dependent conductivity, and of the thermopower is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half- and quarter-filling. The one-dimensional Luttinger liquid is shown to be unstable in the presence of interchain hopping. The results for the metal-insulator transition are compared with other scenarios developed in higher dimensions.
A brief introduction to the bosonization method for interacting one-dimensional fermion systems is given. Using these results, the long-distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu. For infinite U the results are generalized to the case of nonzero nearest-neighbour interaction. The behaviour of thermodynamic quantities, of the frequency-dependent conductivity, and of the thermopower is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half- and quarter-filling. The one-dimensional Luttinger liquid is shown to be unstable in the presence of interchain hopping. The results for the metal-insulator transition are compared with other scenarios developed in higher dimensions.