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arXiv:cond-mat/9512009 · International Journal of Modern Physics B

A CLASS OF COLLECTIVE EXCITATIONS OF THE HUBBARD MODEL: η EXCITATION OF THE NEGATIVE-U MODEL

Eugene Demler, Shoucheng Zhang, NEJAT BULUT, Douglas J. Scalapino

Published Jul 30, 1996• 14 citations
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Abstract

In this series of papers we present a detailed study of the particle-particle collective excitations of the Hubbard model, and their contribution to the density and spin excitation spectrum. In the first paper, we shall investigate the singlet particle-particle pair with momentum (π, π), the η particle, of the negative-U Hubbard model. We review three previously obtained theorems about the η particle and develop a self-consistent linear response theory which takes into account its contribution to the density excitation spectrum in the superconducting state. We show that this self-consistent theory agrees with the exact theorems as well as the results of numerical Monte Carlo simulations.

DOI
10.1142/s0217979296000982

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In this series of papers we present a detailed study of the particle-particle collective excitations of the Hubbard model, and their contribution to the density and spin excitation spectrum. In the first paper, we shall investigate the singlet particle-particle pair with momentum (π, π), the η particle, of the negative-U Hubbard model. We review three previously obtained theorems about the η particle and develop a self-consistent linear response theory which takes into account its contribution to the density excitation spectrum in the superconducting state. We show that this self-consistent theory agrees with the exact theorems as well as the results of numerical Monte Carlo simulations.
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(c) < 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.
Using the formalism introduced by Harris and Lange [Phys. Rev. 157, 295 (1967)] explicit expressions for partial sum rules of the individual Hubbard bands in the large-negative-U limit are derived. The one-particle spectrum, optical spectrum, as well as charge- and spin-response functions are considered. The approach gives a transparent description of the main features of these spectra. The main sum rules depend on only two independent nearest-neighbor expectation values which are estimated in the ground state using numerical calculations, exact results, and linear-spin-wave theory. Simple expressions for the intensities of the upper and lower Hubbard bands in the optical conductivity show that this spectrum is extremely sensitive on details of the ground state. The charge-density wave and superconducting phases are clearly distinguishable and even the transition to the broken-symmetry state may have a detectable influence on the conductivity.
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.
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.
The low-density regime of the two-dimensional Hubbard model has been investigated by the t-matrix approximation, i.e., by taking into account the particle-particle ladder processes represented in terms of particle-particle correlation function, K(q, x+iδ). The q-dependence of K(q, x+iδ) in the region of small x has been examined in detail and it is found that the imaginary part of self-energy function of electrons depends on excitation energy, ε, as ε2ln|ε| which are due to contributions involving K(q, x+iδ) with q≃2kF, kF being the fermi momentum. The existence of the upper Hubbard band for the case of large U has also been demonstrated.
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.