Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

TL;DR

This paper investigates the occurrence of anomalous zeros in the canonical partition function of noninteracting fermions with continuous density of states, revealing unphysical results in certain models and contrasting them with bosonic systems.

Contribution

It identifies and analyzes anomalous Fisher-like zeros in fermionic partition functions, highlighting their unphysical nature in continuous density models.

Findings

Zeros lead to singular free energy and instability

Fermionic zeros are unphysical in harmonic trap models

Bosonic calculations with continuous density are physically sensible

Abstract

Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles. This results in a singular free energy, and instability in other thermal properties of the system. In the context of trapped fermions in a harmonic oscillator, these zeros are shown to be unphysical. By contrast, similar bosonic calculations with continuous density of states yield sensible results.Noninteracting fermions, placed in a system with a continuous density of states yield sensible results.