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Progress of Theoretical Physics

Single-Impurity Anderson Model with Boson Interactions: Zero-Temperature Phase Diagrams

Hiroyuki Kaga, Isamu Sato, M. Kobayashi

Published Dec 1, 1980• 5 citations
Publisher

Abstract

An extended Hartree-Fock (HF) study is made of the effects of boson couplings in the single-impurity Anderson model which was discussed earlier by Haldane with particular reference to multiple solutions and their critical boundaries in relation to mixed ground states in the two-impurity problem. By solving the HF self-consistent equations and calculating energies we construct zero-temperature phase diagrams in parameter space for various boson-coupling constants β.

DOI
10.1143/ptp.64.1918

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An extended Hartree-Fock (HF) study is made of the effects of boson couplings in the single-impurity Anderson model which was discussed earlier by Haldane with particular reference to multiple solutions and their critical boundaries in relation to mixed ground states in the two-impurity problem. By solving the HF self-consistent equations and calculating energies we construct zero-temperature phase diagrams in parameter space for various boson-coupling constants β.
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The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization-group calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
We develop the general many-body perturbation theory for a superconducting quantum dot represented by a single-impurity Anderson model attached to superconducting leads. We build our approach on a thermodynamically consistent mean-field approximation with a two-particle self-consistency of the parquet type. The two-particle self-consistency leading to a screening of the bare interaction proves substantial for suppressing the spurious transitions of the Hartree-Fock solution. We demonstrate that the magnetic field plays a fundamental role in the extension of the perturbation theory beyond the weakly correlated 0 phase. It controls the critical behavior of the $0\text{\ensuremath{-}}\ensuremath{\pi}$ quantum transition and lifts the degeneracy in the $\ensuremath{\pi}$ phase, where the limits to zero temperature and zero magnetic field do not commute. The response to the magnetic field is quite different in 0 and $\ensuremath{\pi}$ phases. While the magnetic susceptibility vanishes in the 0 phase it becomes divergent in the $\ensuremath{\pi}$ phase at zero temperature.
A variety of self-consistent-field techniques have recently been used to calculate correlation functions of the two-dimensional Hubbard model. Such techniques extend Hartree–Fock theory by including a large class of fluctuation processes. The computational requirements of the self-consistent-field approach decrease in lower dimensional systems. For this reason, a thorough test of techniques may be performed by examining the Anderson impurity model, the zero-dimensional limit of the Hubbard model. Using the fluctuation exchange and pseudopotential parquet approximations applied previously in two dimensions, we calculate static and dynamic correlation functions for the Anderson model and compare with quantum Monte Carlo results.
New results are presented for bosons defined on the three-dimensional (3D) cubic lattice at very low temperatures. Calculations are made within the mean-filed (or Hartree) theory applied to the so-called O(2) model. The analysis is used to calculate the zero-temperature phase diagram and determine the critical coupling strength λ for a quantum phase transition. Properties of the zero temperature quantum state, such as: the energy per site, the order parameter, the first possible excitation, and the test single-site phase wave function, are displayed and discussed. Their behavior predicts a transition from an ordered (superfluid) to a disordered (normal/insulating) phase at a critical value of the coupling constant λc = 6.