Evidence for the breakdown of momentum independent many-body t-matrix approximation in the normal phase of Bosons

TL;DR

This paper demonstrates that the momentum independent many-body t-matrix approximation for bosons fails in the normal phase, likely due to neglecting momentum dependence, challenging its previous widespread use.

Contribution

The study reveals the limitations of the momentum independent t-matrix approach for bosons and highlights the importance of including momentum dependence for accurate descriptions.

Findings

The approximation breaks down in the normal phase of bosons.

Neglecting momentum dependence causes the failure of the theory.

The results suggest revising the t-matrix approach to include momentum effects.

Abstract

We revisit the momentum independent many-body t-matrix approach for boson systems developed by Shi and Griffin~\cite{sg} and Bijlsma and Stoof~\cite{bs}. Despite its popularity, simplicity, and expected advantage of being its applicability to both normal and superfluid phases, we find that the theory breaks down in the normal phase of bosons. We conjecture that this failure is due to neglecting of momentum dependence on the t-matrix.