Mott transitions

In this chapter we study the metal-insulator transition which occurs due to correlations between the charge carriers. This quantum phase transitions results from a competition between the parameters of the Hamiltonian which in the present case is the one band Hubbard model with it's two energy scales, the bandwidth W and the Coulomb repulsion U between electrons of opposite spins on the same site. For a fixed density of electrons, n=1, as the ratio U/W increases we expect to find a zero temperature phase transition from a metallic state to an insulator where the electrons are frozen at the lattice sites. The method employed here to investigate this transition is the Gutzwiller approach (Gutzwiller, 1965). This is a variational method which played an important role in providing a framework for the ideas of Mott on the problem of the metal-insulator transition (Mott, 1974). (author)