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Communications in Theoretical Physics

Quantum Impurity Models with Coupled Cluster Method

Jin-Jun Liang, Clive Emary, Tobias Brandes

Published Sep 1, 2010• 0 citations
Publisher

Abstract

We investigate the ground-state properties of the Anderson single impurity model (finite Coulomb impurity repulsion) with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green's function results for the non-interacting model and with Brillouin–Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.

DOI
10.1088/0253-6102/54/3/26

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We investigate the ground-state properties of the Anderson single impurity model (finite Coulomb impurity repulsion) with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green's function results for the non-interacting model and with Brillouin–Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.
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Solving the single-impurity Anderson model is a basic problem of solid state physics.The single-impurity Anderson model is very important, at present it is also used for systems with quantum impurities, e.g.semiconductor quantum dots and molecular transistors.Its main application is in the scheme of dynamical mean eld theory describing strong correlation electron systems.To solve the single-impurity Anderson model problem we use the equation of motion Green function approach.In this report we present the novel equation of motion approximation in which we dierentiate the Green function over both time variables.This diers from the commonly used equation of motion solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable.After extending calculations to higher order Green functions we nd the new approximate dynamical solution of single-impurity Anderson model.The results are compared with the solutions to the single-impurity Anderson model problem at intermediate Coulomb repulsion U such as the modied iterative perturbation theory.Our approach is suitable for describing quantum dots.
High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with s>=1/2s >= 1/2s>=1/2
The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to the application of computational techniques that allow the method to be applied to high orders of approximation using localised approximation schemes, e.g., such as the LSUBmmm scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number s≥12s \ge \frac 12s≥21​. Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.
The coupled-cluster method (CCM) has already been successfully applied by us to anisotropic quantum antiferromagnetic models (XXZ model) with spin s=1/2 in one and two dimensions. This approach is now generalized to the same models but with spin s>1/2. We mainly consider the one-dimensional system in this article. Several systematic approximation schemes developed previously are employed. The ground-state energy is obtained as a function of the spin s and anisotropy. It is found that, for a given approximation that contains long-range contributions, the critical value of the anisotropy for the Heisenberg-Ising phase transition rapidly approaches the classical value of 1 as the spin s increases. We also generalize one of the schemes to a hypercubic lattice of arbitrary dimensionality. By making a detailed comparison with spin-wave theory, perturbation theory, and other variational approaches, some additional intrinsic features of the CCM treatments are emphasized.