Radius of convergence of the hole-line expansion and of the Rayleigh-Schrödinger perturbation series in a solvable model

Abstract

An algebraic approach to the hole-line expansion is reviewed and a general closed-form expression for the n-hole-line contribution to the energy is presented. The precise radius of convergence of the hole-line expansion and of the Rayleigh-Schrödinger perturbation series is calculated in a solvable, yet not trivial model using analyticity arguments. Low-order hole-line approximations up to sixth order are displayed. The radius of convergence of the hole-line expansion is considerably extended as compared to the Rayleigh-Schrödinger series in cases where there is an interplay of short-range repulsion and long-range attraction.