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Physical review. B, Condensed matter

Self-consistent field studies of the negative-UHubbard model

John Luo, N. E. Bickers

Published Dec 1, 1993• 8 citations
Publisher

Abstract

The phase boundary between normal and superconducting phases of the negative-U Hubbard model is obtained within a self-consistent weak-coupling approach known as the ``pseudopotential parquet'' approximation. The shortcomings of simpler self-consistent approaches, including the Hartree-Fock and fluctuation-exchange approximations, are outlined. For intermediate values of U, pseudopotential parquet predicts (i) a maximum in the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ at an electron filling 〈n〉 of approximately 0.92; and (ii) a sharp decrease in ${\mathit{T}}_{\mathit{c}}$ for values of 〈n〉 closer to 1. The scale of transition temperatures is consistent with results from quantum simulations.

DOI
10.1103/physrevb.48.15983

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Physical review. B, Condensed matter•Nov 1, 1996•27 citations
The phase boundary between normal and superconducting phases of the negative-U Hubbard model is obtained within a self-consistent weak-coupling approach known as the ``pseudopotential parquet'' approximation. The shortcomings of simpler self-consistent approaches, including the Hartree-Fock and fluctuation-exchange approximations, are outlined. For intermediate values of U, pseudopotential parquet predicts (i) a maximum in the superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ at an electron filling 〈n〉 of approximately 0.92; and (ii) a sharp decrease in Tc{\mathit{T}}_{\mathit{c}}Tc​ for values of 〈n〉 closer to 1. The scale of transition temperatures is consistent with results from quantum simulations.
We study the negative-U Hubbard model for arbitrary values of the attractive interaction U and band filling by means of the slave-boson mean-field theory. We analyze both the normal and the superconducting states. We show that for the superconducting state our approach gives results similar to those obtained in the usual BCS mean field; only small renormalization of the bare parameters are obtained for U of the order of the bandwidth W. The energy difference between the normal and the superconducting states is maximum for U\ensuremath{\simeq}W. This energy difference is a measure of the superconducting critical temperature, which increases exponentially for small U and decreases as 1/U for large U. We discuss briefly the pair-breaking excitations.
A variety of self-consistent-field techniques have recently been used to calculate correlation functions of the two-dimensional Hubbard model. Such techniques extend Hartree–Fock theory by including a large class of fluctuation processes. The computational requirements of the self-consistent-field approach decrease in lower dimensional systems. For this reason, a thorough test of techniques may be performed by examining the Anderson impurity model, the zero-dimensional limit of the Hubbard model. Using the fluctuation exchange and pseudopotential parquet approximations applied previously in two dimensions, we calculate static and dynamic correlation functions for the Anderson model and compare with quantum Monte Carlo results.
The zero-temperature Hartree theory is extended to finite temperature to investigate the phase diagram, the order parameters, and the chemical potential of the negative-UUU extended Hubbard model in the weak-coupling regime. All the transitions between the charge-ordered, the singlet-superconducting, the mixed, and the nonordered phases are second order. In a special region of the parameter space, we discover the heat-charge-order process, which is the main source for the qualitative difference between the results of the present weak-coupling regime and the strong-coupling regime investigated earlier. Phenomena associated with the heat-charge order are compared to other work in which an effect similar to the heat-charge order exists.
Quantum Monte Carlo simulations are used to explore the phase diagram of the negative-U Hubbard model. As the system is doped away from half filling, 〈n〉=1, the s-wave pair-field correlations are enhanced and the charge-density-wave correlations suppressed. There is no indication of phase separation. Away from half filling, the pair-field correlations are consistent with Kosterlitz-Thouless scaling and a finite Tc{\mathit{T}}_{\mathit{c}}Tc​ which peaks near 〈n〉=1 but vanishes at exactly half filling.
We present fully self-consistent calculations in the fluctuation exchange approximation for the half-filled Hubbard model in two dimensions. A non-Fermi-liquid state evolves with decreasing temperature in this self-consistent model of coupled spin fluctuations and quasiparticles. The mean-field phase transition to long-range antiferromagnetic order is suppressed and we find no evidence of a phase transition to long-range magnetic order. We show that the real part of the self-energy at zero energy shows a positive slope and the imaginary part of the self-energy shows a local minimum. The scale of this structure is set by the zero-temperature gap in mean-field theory. The growth of spin fluctuations is reflected in the evolution of sharply peaked structure in the spin fluctuation propagator around zero energy and Q = (π, π). We present calculations for the Hubbard model in one dimension in a two-particle self-consistent parquet approximation. A second-moment sum rule suggests that vertex corrections to the self-energy are responsible for the greater accuracy of the parquet approximation compared with other self-consistent perturbation theories.
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.