SINGLE-PARTICLE EXCITATIONS IN THE NORMAL-STATE OF THE NEGATIVE-U HUBBARD-MODEL

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.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.

Journal of Physics Condensed MatterJul 25, 19941 citation

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

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

Eugene Demler, Shoucheng Zhang, NEJAT BULUT +1 more

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.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.

arXiv:cond-mat/9512009International Journal of Modern Physics BJul 30, 199614 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

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

SOME PROPERTIES OF THE POSITIVE-U AND NEGATIVE-U HUBBARD MODEL

Francesco Paolo Mancini, M. Marinaro, H. Matsumoto

In this article we review the properties of the 2D Hubbard model by considering at the same time the cases of repulsive and attractive interaction. The paramagnetic solution is studied by means of the composite operator method in the static approximation for the case of half-filling. Some properties of the two models, as the double occupancy and the spin magnetic susceptibility, are calculated for various values of interaction and temperature and compared. In particular, the different role played by thermal fluctuations is analyzed. Analytical and numerical calculations show that there is a critical value of the interaction, Uc, where the system exhibits a metal-insulator transition. At zero temperature it is found that Uc=−W for the negative-U model and Uc≈1.68W for the positive-U model, where W is the band width. At zero temperature, when the strength of the attractive interaction equals the band width, the system exhibits a phase transition to a pair state, where all the electrons are locally paired. The temperature Tp which controls the crossover to the pair state is calculated as a function of U. For strong attractive interaction χ0 is strongly depressed; increases by increasing T and tends to zero as T→TP.In this article we review the properties of the 2D Hubbard model by considering at the same time the cases of repulsive and attractive interaction. The paramagnetic solution is studied by means of the composite operator method in the static approximation for the case of half-filling. Some properties of the two models, as the double occupancy and the spin magnetic susceptibility, are calculated for various values of interaction and temperature and compared. In particular, the different role played by thermal fluctuations is analyzed. Analytical and numerical calculations show that there is a critical value of the interaction, Uc, where the system exhibits a metal-insulator transition. At zero temperature it is found that Uc=−W for the negative-U model and Uc≈1.68W for the positive-U model, where W is the band width. At zero temperature, when the strength of the attractive interaction equals the band width, the system exhibits a phase transition to a pair state, where all the electrons are locally paired. The temperature Tp which controls the crossover to the pair state is calculated as a function of U. For strong attractive interaction χ0 is strongly depressed; increases by increasing T and tends to zero as T→TP.

International Journal of Modern Physics BJun 30, 199613 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.