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Journal of Physics Condensed Matter

Superconducting glass properties in the random infinite-range interaction Hubbard model: stability analysis and phase diagrams

T. K. Kopeć, P. Wróbel

Published Sep 10, 1990• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/2/36/012

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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 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 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 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 influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced
Abstract We investigate a system of interacting bosons with random intersite tunnelling amplitudes. We describe these by introducing Gaussian-distributed hopping integrals into the standard Bose–Hubbard model. This system has been recently shown to exhibit a quantum phase transition to a glassy state. The latter is characterized by a quenched disorder of boson wave-function phases. In this aspect, the system resembles quantum spin-glass systems that attracted much attention. By exploiting this analogy, we employ the well-established methodology originated by Sherrington and Kirkpatrick, which bases on the replica trick and the Trotter–Suzuki expansion. This treatment transforms the original quantum problem into an effective classical one with an additional time-like dimension. Here, we focus on autocorrelation functions of canonical variables of the effective system in the time-like domain. Deep in the disordered phase, we find a highly dynamical nature of correlations in agreement with the expected short memory of the system. This behaviour weakens while approaching and passing the phase boundary, where in the glassy phase asymptotically non-vanishing correlations are encountered. Thus, the state features infinite memory, which is consistent with the quenched nature of glassy disorder with random but frozen boson phases.
We study an experimentally feasible system of strongly correlated bosons with random hoppings described by the infinite-range Bose-Hubbard model on a lattice with hopping integrals given by independent random variables of Gaussian distribution with nonzero mean. We solve this quantum model in the thermodynamic limit, employing the replica method and the Trotter-Suzuki formula. We find and describe a superglass phase that emerges at the interface between glass and superfluid phases. Both glassy and long-range orderings are present in the superglass and compete with each other, as revealed by the anticorrelation of their order parameters. We present phase diagrams in various cross sections of the multidimensional space of system parameters. In selected parameter subspaces, we compare the results to those of nondisordered, diagonally disordered, and once celebrated spin-glass systems.