Quantum Monte Carlo Simulations of Disordered Magnetic and Superconducting Materials
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ABSTRACT Over the last decade, Quantum Monte Carlo (QMC) calculations for tight binding Hamiltonians like the Hubbard and Anderson lattice models have made the transition from addressing abstract issues concerning the effects of electron-electron correlations on magnetic and metal-insulator transitions, to concrete contact with experiment. This paper presents results of applications of "determinant" QMC to systems with disorder such as the conductivity of thin metallic films, the behavior of the magnetic susceptibility in doped semiconductors, and Zn doped cuprate superconductors. Finally, preliminary attempts to model the Kondo volume collapse in rare earth materials are discussed. INTRODUCTION The determinant QMC method[1] is a powerful technique for understanding the physics of itinerant, interacting electrons. Its primary strength is that it treats the correlations between electrons exactly, in contrast to other approaches which resort to various simplifying approximations. The chief disadvantage is its computational cost, which limits the complexity of the models which can be considered. Many of the past applications[2] have been to the single-band two-dimensional Hubbard Hamiltonian. This model is of theoretical interest since it is the simplest lattice Hamiltonian exhibiting both an interaction-driven ("Mott") metal-insulator transition and also long range magnetic order. It is also potentially of importance in understanding the magnetic and superconducting properties of the CuO 2 sheets of high temperature superconductors. That the model has a single band and is in two-dimensions has played a crucial role in making simulations on reasonable lattice sizes (up to 16x16 sites) possible. As algorithms and machine speeds have improved, however, computational restrictions are becoming less prohibitive, and the determinant QMC approach is being applied to tight-binding models which include features such as many orbitals, disorder, and higher dimensionality. In this paper we will provide an overview of four such applications. First, we have studied a model of disordered superconducting films, where there has been a long-standing interest in the possibility of a universal conductivity at the superconductorinsulator phase transition.[3] Second, we examine the effect of topological randomness on magnetically ordered phases, where one issue is the enhancement of the uniform spin susceptibility at low temperatures observed in doped semiconductors.[4] We next describe the behavior of magnetic correlations when non-magnetic impurity sites are introduced, a problem under investigation with recent experiments on Zn doping of ladder compounds 155 Mat. Res. Soc. Symp. Proc. Vol. 491 ©1998 Materials Research Society
and high temperature superconductors.[5] Finally, we describe preliminary results on the phase diagram of the periodic Anderson Hamiltonian in three dimensions.[6] Here the key question is constructing a minimal model which might contain the essential features necessary for describing the "volume-collapse" transi
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