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Physical review. B, Condensed matter

Transfer of spectral weight in the degenerate Hubbard Model in infinite dimension

P. Lombardo, G. Albinet

Published Feb 28, 2002• 8 citations
Publisher

Abstract

Infinite dimensional degenerated Hubbard model has been studied within the framework of the generalized noncrossing approximation. Details on the behavior of excitation spectra are given here, concerning transfer of spectral weight between different energy scales as well as low energy excitation properties. Effective mass evolution close to metal-insulator transitions has been investigated.

DOI
10.1103/physrevb.65.115110

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Infinite dimensional degenerated Hubbard model has been studied within the framework of the generalized noncrossing approximation. Details on the behavior of excitation spectra are given here, concerning transfer of spectral weight between different energy scales as well as low energy excitation properties. Effective mass evolution close to metal-insulator transitions has been investigated.
Using the quantum Monte Carlo technique we compute thermodynamics and spectra for the orbitally degenerate Hubbard model in infinite spatial dimensions. With increasing orbital degeneracy we find in the one-particle spectra broader Hubbard bands (consistent with increased kinetic energy), a narrowing Mott gap, and increasing quasiparticle spectral weight. Hund's rule exchange coupling decreases the critical on-site Coulomb energy for the Mott transition. The metallic regime resistivity for twofold degeneracy is quadratic in temperature at low temperatures.
The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.
We investigate the metal-insulator transitions at finite temperature for the Hubbard model with diagonal alloy disorder. We solve the dynamical mean-field-theory equations with the noncrossing approximation and we use the coherent potential approximation to handle disorder. The excitation spectrum is given for various correlation strength UUU and disorder. Two successive metal-insulator transitions are observed at integer-filling values as UUU is increased. An important selective transfer of spectral weight arises upon doping. The strong influence of the temperature on the low-energy dynamics is studied in detail.
We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.
The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands.