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arXiv:cond-mat/0609717 · Physical Review B

Determinant quantum Monte Carlo study of the screening of the one-body potential near a metal-insulator transition

P. B. Chakraborty, P. J. H. Denteneer, Richard T. Scalettar

Published Mar 26, 2007• 21 citations
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Abstract

In this paper, we present a determinant quantum Monte Carlo study of the two-dimensional Hubbard model with random site disorder. We show that, as in the case of bond disorder, the system undergoes a transition from an Anderson insulating phase to a metallic phase as the on-site repulsion $U$ is increased beyond a critical value ${U}_{c}$. However, there appears to be no sharp signal of this metal-insulator transition in the screened site energies. We observe that, while the system remains metallic for interaction values up to twice ${U}_{c}$, the conductivity is maximal in the metallic phase just beyond ${U}_{c}$ and decreases for larger correlation.

DOI
10.1103/physrevb.75.125117

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In this paper, we present a determinant quantum Monte Carlo study of the two-dimensional Hubbard model with random site disorder. We show that, as in the case of bond disorder, the system undergoes a transition from an Anderson insulating phase to a metallic phase as the on-site repulsion UUU is increased beyond a critical value Uc{U}_{c}Uc​. However, there appears to be no sharp signal of this metal-insulator transition in the screened site energies. We observe that, while the system remains metallic for interaction values up to twice Uc{U}_{c}Uc​, the conductivity is maximal in the metallic phase just beyond Uc{U}_{c}Uc​ and decreases for larger correlation.
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{T}_{c}Tc​ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.
Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transition in the interacting disordered Hubbard model of a Lieb lattice in which the system characterizes the flat band centered at the Fermi level. By choosing suitable electron densities, we ensure the weak interaction sign problem to improve the reliability of our results. It is found that disorder and on-site Coulomb repulsive interaction produce interesting effects that induce the metal-insulator transition which is impossible in the half-filled case. The density of states at the Fermi energy is still finite in the thermodynamic limit, suggesting that the system is an Anderson insulator rather than a Mott insulator. Moreover, this doping system is paramagnetic, unlike the half-filled system which is ferrimagnetic.
We study the temperature-dependent conductivity $\ensuremath{\sigma}(T)$ and spin susceptibility $\ensuremath{\chi}(T)$ of the two-dimensional disordered Hubbard model. Calculations of the current-current correlation function using a quantum Monte Carlo method show that repulsion between electrons can significantly enhance the conductivity, and at low temperatures change the sign of $d\ensuremath{\sigma}/\mathrm{dT}$ from positive (insulating behavior) to negative (conducting behavior). This result suggests the possibility of a metallic phase, and consequently a metal-insulator transition, in a two-dimensional microscopic model containing both interactions and disorder. The metallic phase is a non-Fermi liquid with local moments as deduced from $\ensuremath{\chi}(T)$.
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.
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{V}_{d}/t=0.1Vd​/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|U|/t=5∣U∣/t=5.