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International Journal of Modern Physics B

SUPERCONDUCTING GLASSY STATE IN THE EXTENDED HUBBARD MODEL WITH OFF-DIAGONAL DISORDER

T. K. Kopeć, P. Wróbel

Published Dec 1, 1989• 0 citations
Publisher

Abstract

The phase diagram of the extended Hubbard model with on-site attraction and random inter-site Coulomb energies is studied for the half-filled band case. In the strong coupling limit the problem is mapped onto the system of hard-core bosons (bipolarons) on a lattice, described by the anisotropic pseudo-spin model with infinite-range random exchange interactions—in close analogy with the Sherrington-Kirkpatrick spin glass approach. It is found that the disorder and frustration strongly affects properties of the system leading to the appearance of the bipolaronic superconducting (BSC) phase, the bipolaronic superconducting glass (BSCG) state as well as the bipolaronic charge glass (BCG) phase, depending on the temperature range and the degree of the disorder.

DOI
10.1142/s0217979289001330

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The phase diagram of the extended Hubbard model with on-site attraction and random inter-site Coulomb energies is studied for the half-filled band case. In the strong coupling limit the problem is mapped onto the system of hard-core bosons (bipolarons) on a lattice, described by the anisotropic pseudo-spin model with infinite-range random exchange interactions—in close analogy with the Sherrington-Kirkpatrick spin glass approach. It is found that the disorder and frustration strongly affects properties of the system leading to the appearance of the bipolaronic superconducting (BSC) phase, the bipolaronic superconducting glass (BSCG) state as well as the bipolaronic charge glass (BCG) phase, depending on the temperature range and the degree of the disorder.
The phase diagram of the extended Hubbard model with on-site attraction and random inter-site Coulomb energies is studied for the half-filled band case. In the strong coupling limit the problem is mapped onto the system of hard-core bosons (bipolarons) on a lattice, described by the anisotropic pseudo-spin model with infinite-range random exchange interactions-in close analogy to the Sherrington-Kirkpatrick spin-glass approach. It is found that the disorder and frustration strongly affect properties of the system leading to the appearance of the bipolaronic superconducting phase, the bipolaronic superconducting glass state as well as the bipolaronic charge glass phase, depending on the temperature range and the degree of the disorder.
The extended Hubbard model with on-site attraction and random infinite-range inter-site Coulomb interaction is studied for arbitrary band filling. In the strong-coupling limit the problem is mapped onto a system of hard-core bosons (local electron pairs) on a lattice described by the anisotropic pseudo-spin model with infinite-range random interactions-in close analogy to the standard Sherrington-Kirkpatrick spin-glass approach. With the use of thermofield dynamics as a substitute for the 'n-replica trick', and a one-loop approximation for the dynamic self-interaction, the stability of the mean-field-type solution with respect to the action of fluctuations is investigated in the parameter space including the temperature, degree of disorder and band-filling parameter.
The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
The half-filled attractive Hubbard model exhibits a simultaneous charge-density wave and superconducting order in its ground state. In this paper we use approximation-free quantum Monte Carlo techniques to explore the effect of disorder in the site energies on this degeneracy. We find that superconducting order survives randomness out to a critical amount of disorder, but charge ordering is immediately destroyed. This settles the issue as to whether disordered site energies, which do not break time-reversal invariance, can destroy pairing correlations. We also locate the precise ratio of disorder to bandwidth required for the disorder-driven transition from the superconducting state. We explore the validity of a strong-coupling picture which maps the system onto a Heisenberg model in a random magnetic field.
The phase diagrams and electron orderings of the half-filled extended Hubbard models with anisotropic spin-exchange interactions (J⊥, J||) are studied. The cases of ferromagnetic (Jα 0) exchange couplings are considered for repulsive on-site interaction (U ≥ 0). The analysis of these t–U–J||–J⊥ models is performed for d-dimensional hypercubic lattices including d = 1 and d = ∞ by means of the (broken symmetry) HFA supplemented, for d = ∞, by the slave-boson mean-field method. The basic features of the derived phase diagrams are discussed.
The extended Hubbard model with nearest neighbour inter-site correlations has been studied by mapping it onto a spin-Hamiltonian. In the case of a half-filled band the problem is equivalent to that of an anisotropic Heisenberg model in the absence of a field. The phases in the U-Q plane obtained here are in good agreement with those obtained by Monte Carlo simulation. The antiferromagnetic XY-ordered phase of the model is shown to be very similar to an RVB phase. Extending the analogy away from half-filling, a possible dependence of the critical temperature T c with the doping concentration delta in a high-T c system is suggested.