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Journal de physique

Equivalence of the perturbative and Bethe-Ansatz solution of the symmetric Anderson Hamiltonian

B. Horvatié, V. Zlatié

Published Jan 1, 1985• 43 citations
Publisher

Abstract

We show that the exact Bethe-Ansatz results for the spin and charge susceptibilities and the specific heat for the symmetric Anderson model can be expanded in power series which converge absolutely for any finite value of the expansion parameter U/πΔ and which coincide with Yosida and Yamada's perturbative expansions for the same quantities. The coefficients of these expansions are found to satisfy the simple recursion relation Cn = (2 n — 1) Cn-1 - (π/2)2 Cn-2 and to decrease rapidly with increasing order. Hence a small number of terms proves sufficient for an accurate description of the system even in the strong correlation regime (U/πΔ ≳ 2). Finally, we discuss an attempt to construct a perturbative solution for the ground state of the asymmetric Anderson Hamiltonian.

DOI
10.1051/jphys:019850046090145900

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Using functional methods and the exact renormalization group we derive Ward identities for the Anderson impurity model. In particular, we present a non-perturbative proof of the Yamada–Yosida identities relating certain coefficients in the low-energy expansion of the self-energy to the thermodynamic particle number and spin susceptibilities of the impurity. Our proof underlines the relation of the Yamada–Yosida identities to the U (1) × U (1) symmetry associated with the particle number and spin conservation in a magnetic field.
Building an effective Hamiltonian utilizing a projector-operatorprocedure, we derive an approximation based on a selfconsistenthybridization expansion to study the ground stateproperties of the Anderson Impurity model.We applied the approximationto the general case of finite Coulomb repulsionU, extending previous work with the same formalism in theinfinite-U case. The ground state energy and their related zerotemperature properties are accurately obtained in the case inwhich U is large enough, but still finite, as compared with the rest of energy scales involved in the model. The results for thevalence of the impurity are compared with exact results thatwe obtain from equations derived using the Bethe ansatz andwith a perturbative approach. The magnetization and magneticsusceptibility is also compared with Bethe ansatz results. Inorder to do this comparison, we also show how to regularizethe Bethe ansatz integral equations necessary to calculate theimpurity valence, for arbitrary values of the parameters.
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