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arXiv:cond-mat/0607427 · Physical Review B

Mott and band-insulator transitions in the binary-alloy Hubbard model: Exact diagonalization and determinant quantum Monte Carlo simulations

Norman Paris, A. Baldwin, Richard T. Scalettar

Published Apr 19, 2007• 14 citations
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Abstract

We use determinant quantum Monte Carlo simulations and exact diagonalization to explore insulating behavior in the Hubbard model with a bimodal distribution of randomly positioned local site energies. From the temperature dependence of the compressibility and conductivity, we show that gapped, incompressible Mott insulating phases exist away from half-filling when the variance of the local site energies is sufficiently large. The compressible regions around this Mott phase are metallic only if the density of sites with the corresponding energy exceeds the percolation threshold, but are Anderson insulators otherwise.

DOI
10.1103/physrevb.75.165113

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We use determinant quantum Monte Carlo simulations and exact diagonalization to explore insulating behavior in the Hubbard model with a bimodal distribution of randomly positioned local site energies. From the temperature dependence of the compressibility and conductivity, we show that gapped, incompressible Mott insulating phases exist away from half-filling when the variance of the local site energies is sufficiently large. The compressible regions around this Mott phase are metallic only if the density of sites with the corresponding energy exceeds the percolation threshold, but are Anderson insulators otherwise.
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Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x1+x1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc{U}_{c}Uc​ at which the metal-insulator transition occurs.
We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo. At half-filling, when the interaction strength or the staggered potential dominates, we find Mott and band insulators, respectively. When these two energies are of the same order, we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
We present a numerical solution of the infinite-dimensional Hubbard model at finite temperature in the paramagnetic phase. The problem reduces to a single-impurity Anderson model supplemented by a self-consistency condition. Using Monte Carlo methods and complete enumeration we determine the imaginary-time Green's function, the density of doubly occupied sites, and the compressibility close to half filling. All three quantities present direct evidence for a Mott insulating phase above a critical value of U.
Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra A(ω,k)A(ω, k)A(ω,k) show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy ωωω and momentum kkk with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around (π,0)(π, 0)(π,0) and (0,π)(0, π)(0,π) momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around (π,0)(π,0)(π,0) and (0,π)(0,π)(0,π) with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in A(ω,k)A(ω, k)A(ω,k) show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.