Quantum Critical Point of Hubbard Model in Finite Dimensions

The Hubbard model, at various dimensions, shows to have signs of a quantum critical point. By using Dynamical Mean Field Theory signals of a quantum critical point, for the Hubbard model in infinite dimensions, can be seen through ω/t scaling of the local spin susceptibility. In finite dimensions, Dynamical Cluster Approximation gives insight into the Hubbard model. The quasiparticle weight of the 2D Hubbard model shows evidence of a quantum critical point. As doping increases, the quasiparticle weight exhibits the change from non-Fermi liquid, to marginal Fermi liquid, and eventually to Fermi liquid. The existence of a singular density of state of the 2D model may facilitate an anti-ferromagnetic fluctuations and the formation of a pseudogap. As the 3D density of states does not contain a Van Hove singularity, it is an interesting model for the study of quantum criticality. We investigate the relationship of the quantum critical point in 3D and its similarities to points in other dimensions.