Quantum Phase Transition in the Infinite Dimensional Hubbard Model

We investigated the ground state of the infinite dimensional Hubbard model for both attractive and repulsive interactions by applying Gutzwiller type variational wave functions. Our variational wave functions have lower energies than the simple BCS wave function for the attractive case, and lower energies than the Brinkman-Rice state for the repulsive case. We found that the system has several phases depending on the density of electrons and the interaction strength. Investigated phases include antiferromagnetic, Fermi liquid, superconducting, charge density wave, and supersolid phases. The last one is a coexistence phase of superconducting and charge density wave states.