Gutzwiller Variational Method

Finding the ground-state energy and many-body properties of strongly correlated systems, such as Mott insulators and high temperature superconductors, is currently a very important part of theoretical physics. In these materials, electron-electron correlations play a leading role in determining the phase diagram and other interesting physical properties. One of the most important model Hamiltonian methods to study these strongly-correlated systems is the Hubbard model. We use the Gutzwiller variational method, a well-known technique to find ground-state energy of correlated systems, to solve the one dimensional Hubbard model. In this problem, the Hamiltonian contains the kinetic energy of electrons from simple tight-binding method, and onsite Coulomb interaction between two electrons occupying the same lattice site. We compare the results of Gutzwiller variational method for the ground-state energy of the system with two other methods, Hartree approximation and Exact-Diagonalization.