Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity

TL;DR

This paper uses renormalization group techniques to analyze finite-size and particle-number effects in an ultracold Fermi gas at unitarity, providing insights into universal quantities and their dependence on system size.

Contribution

It offers a quantitative assessment of finite-size effects on universal properties like the Bertsch parameter and fermion gap using RG methods.

Findings

Bertsch parameter saturates quickly with increasing system size.

Fermion gap shows strong dependence on system size, especially at small pairing sources.

Results aid in understanding finite-size effects in Monte Carlo simulations.

Abstract

We investigate an ultracold Fermi gas at unitarity confined in a periodic box $V=L^3$ using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finite-size and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.