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Physical review. B, Condensed matter

Excitation spectrum of the attractive Hubbard model

R. Micnas, M. H. Pedersen, Sandra Schafroth, T. Schneider, José Jesús Rodríguez-Núñez, H. Beck

Published Dec 1, 1995• 86 citations
Publisher

Abstract

We study excitation-spectrum and normal-state properties of the two-dimensional attractive Hubbard model using the conserving, self-consistent T-matrix formalism in the intermediate coupling regime and at low electron concentration. Numerical results are presented for one-particle and two-particle excitation spectra, the one-particle momentum distribution, the chemical potential, and the static spin susceptibility. For a coupling strength of U/t=4.0, the one-particle spectral function, A(k,\ensuremath{\omega}), shows two peaks of different weights. One peak can be associated with pair formation, whereas the other corresponds to renormalized quasiparticle excitation. It turns out that the two-band feature is reasonably well described by an ansatz for A(k,\ensuremath{\omega}), which satisfies the first four frequency moments.

DOI
10.1103/physrevb.52.16223

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We study excitation-spectrum and normal-state properties of the two-dimensional attractive Hubbard model using the conserving, self-consistent T-matrix formalism in the intermediate coupling regime and at low electron concentration. Numerical results are presented for one-particle and two-particle excitation spectra, the one-particle momentum distribution, the chemical potential, and the static spin susceptibility. For a coupling strength of U/t=4.0, the one-particle spectral function, A(k,\ensuremath{\omega}), shows two peaks of different weights. One peak can be associated with pair formation, whereas the other corresponds to renormalized quasiparticle excitation. It turns out that the two-band feature is reasonably well described by an ansatz for A(k,\ensuremath{\omega}), which satisfies the first four frequency moments.
We constructed the one-particle spectral functions (diagonal and off-diagonal) which reproduce BCS for weak coupling and which take into account the effect of correlations on superconductivity in the attractive Hubbard model. The diagonal spectral function is composed of three peaks and the off-diagonal one is composed of two peaks. This ansatz satisfies the sum rules for the first six moments. Our solutions are valid for intermediate coupling, i.e., for U/t ≈ −4.0. Our set of analytical equations for the unknown variables is self-consistent and has been solved numerically in lowest order of the order parameter. As a result, we obtain that the presence of the third band, or upper Hubbard band, strongly renormalizes the two lower bands, making that the energy gap be k-dependent while the order parameter is pure s-wave. This shows that the order parameter and the gap are two different quantities.
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.
One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak-coupling regime using the non-self-consistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real-frequency axis. For temperatures sufficiently close to the superconducting transition temperature, a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.
We calculate the one-electron spectral function of the attractive (negative-U)U)U) Hubbard model. We work in the intermediate-coupling and low-density regime and obtain the self-energy in an approximate analytical form. The excitation spectrum is found to consist of three branches. The results are obtained in a framework based on the self-consistent TTT-matrix approximation, which is compatible with the Mermin-Wagner theorem.
One-particle properties of the normal state of a negative-U Hubbard model are analysed within the framework of the incoherent local-pair (ILP) approach. In the self-consistent Hartree-Fock approximation an analytic expression for the critical value U<0 of the coupling strength is obtained below which the system becomes unstable towards the formation of incoherent local pairs. The single-particle excitation spectrum for different regimes of the attraction strength U and particle concentration n is investigated, and the U-n phase diagram is discussed.
Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T -matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presence of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behaviour. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to the experimental observations for the cuprates.