We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction
f of sites, while keeping a finite
U on the remaining ones. Through quantum Monte Carlo simulations for several values of
f and
U and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor
Ps and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for
Ps have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration
fc, which increases with
U, at least up to
U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of
f shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of
f for
U=3, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest
Tc increasing with
U in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.
The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with
s-wave pairing order. However,
Tc is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents determinant quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential
Vtrap which makes the fermion density $\ensuremath{\rho}$ inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density $\ensuremath{\rho}(\mathbit{i})$ passes through one fermion per site. In this ring of $\ensuremath{\rho}(\mathbit{i})=1$, charge order is enhanced. A comparison is made between treating
Vtrap within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.
We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above
Tc and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.
We investigate the competition between superconductivity (SC) and charge density wave (CDW) under a time-dependent periodic field in the attractive Hubbard model. By employing the time-dependent exact diagonalization method, we show that the driving frequency and amplitude of the external field can control the enhancement of either the superconducting pair or the CDW correlation in the system, for which SC and CDW are degenerate in the ground state of the half-filled attractive Hubbard model in the absence of the field. In the strong-coupling limit of the attractive Hubbard interaction, the controllability is characterized by the anisotropic interaction of the effective model. The anisotropy is induced by the external field and lifts the degeneracy of SC and CDW. We find that the enhancement or suppression of the superconducting pair and CDW correlations in the periodically driven attractive Hubbard model can be well interpreted by the quench dynamics of the effective model derived in the strong-coupling limit.
The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the past several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.
In previous studies of the half-filled bilayer attractive Hubbard model [Prasad et al., Phys. Rev. A 89, 043605 (2014); Prasad, Phys. Rev. B 106, 184506 (2022)], it has been shown that the clean system has a band-insulator (BI) to superfluid (SF) quantum phase transition. In this paper, we append the effects of random on-site disorder on the kinetic energy, double occupancy, and the pair-pair correlations in the bilayer model. Using the determinant quantum Monte Carlo simulation, we observe that the on-site random disorder plays a significant role in the localization of on-site pairs, and hence in the reduction of the effective hopping. This results in an increase of the double occupancy, which is an effect that is similar to the attractive interaction. We find no change in the critical value of the interaction at which the model undergoes a transition from the BI to SF regime, even though the pair-pair correlations get suppressed for finite on-site disorder strengths
Vd/t=0.1--0.8. We also confirm that the weak-disorder suppresses the SF phase largely in the strong-coupling limit. Hence the region of the SF phase reduces in the presence of random on-site disorder. Finally, through finite-size scaling, we have estimated the critical disorder strength ${V}_{d}^{c}/t\ensuremath{\sim}1.44$ at
∣U∣/t=5.