Fisher zeros of a unitary Bose gas

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.

7 pages, 7 figures

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• Efimov correlations in strongly interacting Bose gases
• Lee-Yang zeros and two-time spin correlation function
• Lee-Yang theory of the Curie-Weiss model and its rare fluctuations
• Two-time correlation functions and the Lee-Yang zeros for an interacting Bose gas
• Measuring complex partition function zeroes of Ising models in quantum simulators
• Lee-Yang theory of the two-dimensional quantum Ising model
• Lee-Yang theory of Bose-Einstein condensation
• Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin
• Probing the Lee-Yang zeros of a spin bath by correlation functions and entanglement of two spins
• Time correlation functions and Fisher zeros for q-deformed Bose gas
• Determination of melting temperature of hexagonal ice using Lee-Yang phase transition theory
• Padé Approximation and Partition Function Zeros
• Detecting the purely imaginary Fisher zeros of an Ising spin system on a quantum computer