Series expansion for the symmetric Anderson Hamiltonian

Abstract

Spin susceptibility, charge susceptibility, and specific heat for the symmetric Anderson model can be expanded in power series which converge absolutely for any finite value of the expansion parameter $\frac{U}{\pi \Delta }$. The coefficients of these expansions satisfy the simple recursion relation $C_n=(2n-1)\mathrm{}{C}_{n-1\mathrm{}}-{\left(\frac{\pi }{2}\right)}^2 C_{n-2\mathrm{}}$. The expansions rapidly assume their asymptotic form and the scaling behavior is obtained for $\frac{U}{\pi \Delta }\gtrsim 2$.