Metal-Insulator transition in the Generalized Hubbard model

TL;DR

This paper provides an exact solution for the ground state of a generalized Hubbard model, identifying conditions for ferromagnetism and the metal-insulator transition, with specific solutions in one dimension.

Contribution

It introduces an exact analytical approach to the generalized Hubbard model, revealing ferromagnetic ground states and critical parameters for the metal-insulator transition.

Findings

Existence of ferromagnetic ground state for one hole and one double occupied site

Determination of critical on-site repulsion for metal-insulator transition

Exact solutions for special parameter values in one-dimensional case

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.