Fisher zeros of a unitary Bose gas

TL;DR

This paper investigates the Fisher zeros of a unitary Bose gas, revealing how phase transition signatures like Bose-Einstein condensation are affected by strong interactions and how these zeros relate to thermodynamic properties.

Contribution

It provides an exact formulation of Fisher zeros for a strongly interacting unitary Bose gas using virial expansion, showing the persistence of BEC and the shift in condensation temperature.

Findings

Fisher zeros form curves indicating phase transitions in Bose gases.

Strong interactions shift the BEC temperature lower.

Fisher zeros analysis aligns with heat capacity calculations.

Abstract

For real inverse temperature beta, the canonical partition function is always positive, being a sum of positive terms. There are zeros, however, on the complex beta plane that are called Fisher zeros. In the thermodynamic limit, the Fisher zeros coalesce into continuous curves. In case there is a phase transition, the zeros tend to pinch the real-beta axis. For an ideal trapped Bose gas in an isotropic three-dimensional harmonic oscillator, this tendency is clearly seen, signalling Bose-Einstein condensation (BEC). The calculation can be formulated exactly in terms of the virial expansion with temperature-dependent virial coefficients. When the second virial coefficient of a strongly interacting attractive unitary gas is included in the calculation, BEC seems to survive, with the condensation temperature shifted to a lower value for the unitary gas. This shift is consistent with a direct calculation of the heat capacity from the canonical partition function of the ideal and the unitary gas.