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.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.

Sep 10, 20260 citations

Excitation spectrum of the attractive Hubbard model

R. Micnas, M. H. Pedersen, Sandra Schafroth +3 more

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 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.

Physical review. B, Condensed matterDec 1, 199586 citations

One-electron spectral functions of the attractive Hubbard model for intermediate coupling

M. Yu. Kagan, Raymond Frésard, Massimiliano Capezzali +1 more

We calculate the one-electron spectral function of the attractive (negative- $U)$ 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 $T$ -matrix approximation, which is compatible with the Mermin-Wagner theorem.We calculate the one-electron spectral function of the attractive (negative-$U)$ 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 $T$-matrix approximation, which is compatible with the Mermin-Wagner theorem.

arXiv:cond-mat/9704136Physical review. B, Condensed matterMar 1, 199847 citations

Superconducting properties of the attractive Hubbard model: A slave-boson study

Bogdan R. Bułka, Stanisl aw Robaszkiewicz

The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterNov 1, 199627 citations

Pair-fluctuation-induced pseudogap in the normal phase of the two-dimensional attractive Hubbard model at weak coupling

Daniel Rohe, Walter Metzner

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.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.

arXiv:cond-mat/0011500Physical review. B, Condensed matterMay 22, 200147 citations

The singlet state in the Hubbard model with U=∞

E. V. Kuz’min, I. O. Baklanov

We discuss, in connection with the problem of the ground state in the Hubbard model with U =∞, the normal (nonmagnetic) N -state of a system over the entire range of electron concentrations n ≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε 0 ( n ) of the N -state is lower than the energy ε FM ( n ) of a saturated ferromagnetic state for all values of n . Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N -state is stable for all values of n . A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T =0 acquires a Migdal discontinuity, whose magnitude depends on n . The energy of the N -state in this approximation is still lower than ε FM ( n ) for n <1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n . Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state.We discuss, in connection with the problem of the ground state in the Hubbard model with U =∞, the normal (nonmagnetic) N -state of a system over the entire range of electron concentrations n ≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε 0 ( n ) of the N -state is lower than the energy ε FM ( n ) of a saturated ferromagnetic state for all values of n . Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N -state is stable for all values of n . A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T =0 acquires a Migdal discontinuity, whose magnitude depends on n . The energy of the N -state in this approximation is still lower than ε FM ( n ) for n <1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n . Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state.

Journal of Experimental and Theoretical PhysicsDec 1, 19980 citations

We calculate the one-electron spectral function of the attractive (negative-

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

T

-matrix approximation, which is compatible with the Mermin-Wagner theorem.