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

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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

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