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Journal of the Physical Society of Japan

One-Particle Spectral Weightof the Two-Dimensional Hubbard Modelin thet-Matrix Approximation

Osamu Narikiyo, Kazumasa Miyake

Published Jul 15, 1995• 4 citations
Publisher

Abstract

The one-particle spectral weight of the two-dimensional Hubbard model is studied in the t -matrix approximation. A single quasi-particle peak is obtained in the spectrum so that the quasi-particle picture holds in the t -matrix approximation, while in the second-order perturbation (H. Fukuyama and M. Ogata: J. Phys. Soc. Jpn. 63 (1994) 3923) it is concluded that splitting of the spectral weight occurs.

DOI
10.1143/jpsj.64.2290

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Physical review. B, Condensed matter•Jul 15, 1995•34 citations
The one-particle spectral weight of the two-dimensional Hubbard model is studied in the t -matrix approximation. A single quasi-particle peak is obtained in the spectrum so that the quasi-particle picture holds in the t -matrix approximation, while in the second-order perturbation (H. Fukuyama and M. Ogata: J. Phys. Soc. Jpn. 63 (1994) 3923) it is concluded that splitting of the spectral weight occurs.
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 have calculated the single-particle density of states N(\ensuremath{\omega}) and the spectral weight A(p,\ensuremath{\omega}) for the doped two-dimensional Hubbard model by combining quantum Monte Carlo simulations with the maximum-entropy analytic continuation technique. We present results for various values of the doping, temperature, and Coulomb repulsion U. For sufficiently strong Coulomb repulsions and near half filling, a Mott-Hubbard pseudogap exists. In this case, we find that a peak develops at the top of the lower Hubbard band near the Fermi level at temperatures of order of the hopping t. The structure of this peak is similar to that seen in the infinite dimensional Hubbard model.
The quasi-particle spectral weight at the Fermi level (Z(F)) in the two-dimensional (2D) electron gas is determined as a function of density. A model local field correction factor (G(q)) possessing the correct features both in the small and large q limits is introduced and used to calculate the Z(F), by evaluating the electron self-energy within the GW approximation. It is found that the Z(F) calculated using the present G(q) is smaller than the one calculated using the Hubbard G(q) implying that the correlation interaction makes the system more localized. Our result also indicates that high T(c) superconductors, if described by a 2D electron gas system, will exhibit a small but nonzero (approximately 0.2) quasi-particle spectral weight at the Fermi level.
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 calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.