arXiv subjects
Publications and source records attributed to Gabriel Kotliar.
We derive a new perturbation scheme for treating the large d limit of lattice models at arbitrary filling. The results are compared with exact diagonalization data for the Hubbard model and found to be in good agreement.
We study the metal-to-insulator transition of the Hubbard model at zero temperatures in infinite dimensions. The coexistence of metallic and insulating solutions for a finite range of the interaction is established. It is shown that the metallic solution is lower in energy for any interaction in the coexistence region and that the transition is of second order.
We introduce a systematic low-energy approach to strongly correlated electron systems in infinite dimensions, and apply it to the problem of the correlation-induced metal-insulator transition in the half-filled Hubbard model. We determine the low-energy scaling functions of the metallic state, including the single-particle Green function and dynamical spin susceptibility, as well as thermodynamic properties and relate them to experimental data in transition metal oxides.
We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the local physics at different energy scales. For a metallic system away from half-filling, the fixed point local Hamiltonian is a generalized Anderson impurity model in the mixed valence regime. There are three types of fixed points: a coherent Fermi liquid (FL) and two classes of self-similar (scale invariant) phases which we denote incoherent metallic states (IMS). When the transitions between the atomic configurations proceed coherently at low energies, the system is a Fermi liquid. Incoherent transitions between the low energy atomic configurations characterize the incoherent metallic states. The initial conditions for the renormalization group flow are determined by the physics at rather high energy scales. This is the domain of local quantum chemistry. We use simple quantum chemistry estimates to specify the basin of attraction of the IMS fixed points.
We study an extended Hubbard model in the limit of infinite dimensions and its zero dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: a) the usual strong coupling state in which a resonance forms at the Fermi level; b) a weak coupling state in which neither the impurity spin nor the impurity charge degrees of freedom is quenched; and c) an intermediate coupling state where the spin but not the charge degree of freedom is quenched. The corresponding phases of the extended Hubbard model in infinite dimensions are a) a Fermi liquid; b) a non-Fermi liquid state with incoherent charge and spin excitations; and c) a non-Fermi liquid state with incoherent charge but coherent spin excitations. The non-Fermi liquid phases are incoherent metallic states with vanishing quasiparticle residue, self-similar local correlation functions, and asymptotically decoupled charge and spin excitations. The non-Fermi liquid phases occur for a wide range of parameters.
We study a two-band Hubbard model in the limit of infinite dimensions, using a combination of analytical methods and Monte-Carlo techniques. The normal state is found to display various metal to insulators transitions as a function of doping and interaction strength. We derive self-consistent equations for the local Green's functions in the presence of superconducting long-range order, and extend previous algorithms to this case. We present direct numerical evidence that in a specific range of parameter space, the normal state is unstable against a superconducting state characterized by a strongly frequency dependent order-parameter.