General solution to the Kohn-Luttinger nonconvergence problem

TL;DR

This paper presents a general method to resolve the nonconvergence issue in finite-temperature many-body perturbation theory as temperature approaches zero, by modifying the reference wave function, demonstrated through numerical examples.

Contribution

It introduces a simple, general solution to the Kohn-Luttinger nonconvergence problem by altering the reference wave function, applicable across various perturbation orders.

Findings

Nonconvergence can be avoided by changing the reference wave function.

Numerical illustrations up to fifth-order perturbation theory confirm the effectiveness.

The proposed solution is simple and broadly applicable.

Abstract

A simple, but general solution is proposed for the Kohn-Luttinger problem, i.e., the nonconvergence of the finite-temperature many-body perturbation theory with its zero-temperature counterpart as temperature is lowered to zero under some circumstances. How this nonconvergence can be avoided by altering the reference wave function is illustrated numerically by using up to the fifth order of the perturbation theory.