Special CM/AMO Seminar | Large Cluster Dynamical Mean Field Simulations for Hubbard Models, Emanuel Gull, Ph.D. (Max Planck Institute for the Physics of Complex Systems)

Emanuel Gull, Ph.D. (Max Planck Institute for the Physics of Complex Systems)

Newly developed computational methods and an increase in computational power have enabled cluster dynamical mean field calculations of the Hubbard model with interaction strengths and band structures representative of high temperature superconductors, for clusters large enough that the thermodynamic limit may be determined. We present the methods, show how they can be controlled and how extrapolations to the thermodynamic limit work in practice. We show that the two-dimensional Hubbard model with next-nearest neighbor hopping at intermediate interaction strength captures much of the exotic behavior characteristic of the high temperature superconductors. An important feature of the results is a pseudogap for hole doping but not for electron doping. The pseudogap regime is characterized by a gap for momenta near the Brillouin zone face and gapless behavior near the zone diagonal. We also present results for the superconducting regime and we calculate spectra, self-energies, and – using a formalism to include vertex corrections – response functions for Raman spectroscopy and optical conductivities. We compare our results to experiment and show that we are in good agreement.