The partition function of an interacting many body system: beyond the perturbed static path approximation

TL;DR

This paper extends the perturbed static path approximation to lower temperatures for many-body systems, addressing instabilities and providing accurate results for models like the Lipkin model, with applications in nuclear physics and mesoscopic systems.

Contribution

It introduces a systematic extension of PSPA that remains valid at low temperatures by handling classical mean field instabilities.

Findings

Accurately approximates the level density of the Lipkin model at low temperatures.

Successfully tests the extended PSPA against exact solutions for specific models.

Addresses divergences in conventional PSPA due to mean field instabilities.

Abstract

Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures. Thereby, special attention must be paid to instabilities of the classical mean field solution in functional space that cause divergencies within the conventional PSPA. As a result we develop an approximation applicable from high to very low temperatures. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin model. In particular, we obtain a very good approximation to the level density of the Lipkin model even at low thermal excitations. Our results may have potential applications in low temperature nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. PACS: 5.30.-d, 24.60.-k, 21.10.Ma, 74.25.Bt