Correlation between Lanczos Method and Exact Diagonalisation Method in the Study of Highly Correlated Electrons System

The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. The Hubbard model, named after John Hubbard 1963, is the simplest model of interacting particles in lattices, with the only two tennis in the Hamiltonian; a kinetic term allowing for hopping of particles between soles of the lattice and a potential term consisting of an on sites interaction. The particles can either be fermions or bosons.

The Hubbard model is a good approximate for particles in a periodic potential at sufficiently low temperature that all the particles are in the lowest Bloch band, as long as any long-range interactions between the particles can be ignored. If interaction between particles on different sites of the lattice are included, the model is often referred to as the extended Hubbard model .The model was originally proposed to describe electrons in solids and has since been the focus of particular interest as a model for high temperature super conductivity. Read more>>>>>>>>>>>>>>>