Disorder- and correlation-driven metal-insulator transitions

Metal-insulator transitions driven by disorder (Delta) and/or by electron correlations (U) are investigated within the Anderson-Hubbard model with local binary-alloy disorder using a simple but consistent mean-field approach. The Delta-U phase diagram is derived and discussed for T=0 and finite temperatures.Comment: 2 pages, 2 figures, submitted to the SCES'04, Ref.4 update

Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function

The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to get the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss the efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.Comment: 20 pages, 5 figures, v2 with minor corrections, JPCM in pres

Non-equilibrium cluster-perturbation theory

The cluster perturbation theory (CPT) is one of the simplest but systematic quantum cluster approaches to lattice models of strongly correlated electrons with local interactions. By treating the inter-cluster potential, in addition to the interactions, as a perturbation, it is shown that the CPT can be reformulated as an all-order re-summation of diagrams within standard weak-coupling perturbation theory where vertex corrections are neglected. This reformulation is shown to allow for a straightforward generalization of the CPT to the general non-equilibrium case using contour-ordered Green's functions. Solving the resulting generalized CPT equation on the discretized Keldysh-Matsubara time contour, the transient dynamics of an essentially arbitrary initial pure or mixed state can be traced. In this way, the time-dependent expectation values of one-particle observables can be obtained within an approximation that neglects spatial correlations beyond the extension of the reference cluster. The necessary computational effort is very moderate. A detailed discussion and simple test calculations are presented to demonstrate the strengths and the shortcomings of the proposed approach. The non-equilibrium CPT is systematic and is controlled in principle by the inverse cluster size. It interpolates between the non-interacting and the atomic or decoupled-cluster limit which are recovered exactly and is found to predict the correct dynamics at very short times in a general non-trivial case. The effects of initial-state correlations on the subsequent dynamics and the necessity to extend the Keldysh contour by the imaginary Matsubara branch are analyzed carefully and demonstrated numerically. It is furthermore shown that the approach can describe the dissipation of spin and charge to an uncorrelated bath with an essentially arbitrary number of degrees of freedom.Comment: 14 pages, 9 figure

On a Dual Pair of Spaces of Smooth and Generalized Random Variables

A dual pair G and G* of smooth and generalized random variables, respectively, over the white noise probability space is studied. G is constructed by norms involving exponentials of the Ornstein-Uhlenbeck operator, G* is its dual. Sufficient criteria are proved for when a function on S(IR) is the S-transform of an element in G or G*

Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio

Microbial iron reduction during passive in situ remediation of an acidic mine pit lake mesocosm

AbstractFerric iron reduction was studied in a pilot-scale enclosure experiment for passive biological remediation of an acidic mine pit lake in Lusatia, Germany. The metabolic properties of prokaryotes involved in Fe(III) reduction may be important for the outcome of biological remediation, as chemolithotrophic Fe(III) reduction can counteract the desired pH increase, but heterotrophic Fe(III) reduction will provide the necessary Fe(II) for precipitation of sulfide minerals following sulfate reduction. Therefore, vertical profiles of sediment parameters related to iron and sulfur cycling were determined in conjunction with viable counts of different ferric iron-reducing micro-organisms using selective media. Findings were compared to an untreated reference site. The addition of organic matter stimulated ferric iron reduction and sulfate reduction in the enclosure and led to elevated pH and accumulations of ferrous iron and reduced sulfur compounds. Numbers of neutrophilic heterotrophic Fe(III) reducers increased during treatment, those of acidophilic heterotrophic Fe(III) reducers remained similar, and those of acidophilic chemolithotrophic Fe(III) reducers decreased. Zones of ferric iron-reducing activity corresponded well with microbial depth profiles; however, viable counts of neutrophilic or acid-tolerant Fe(III) reducers must have been underestimated based on the corresponding observed activity levels. Ferric iron reduction by chemolithotrophic acidophiles seemed to be of minor importance, so a lowering of pH values due to Fe(III) reducing activity is unlikely