Finite-size and particle-number effects in an ultracold Fermi gas at unitarity

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 finitesize and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.

Dimensional crossover of nonrelativistic bosons

“…The FRG approach has been applied to study the effect of compactified dimensions on many-body system both in several relativistic and non-relativistic setups. Finite volume effects, i.e., when all spatial directions are confined to a cube of size [0, L] d , have been studied for quarkmeson-models [46][47][48][49] and the 3D BCS-BEC crossover [50]. In particular, Ref.…”

Phase Structure of Strongly Interacting Theories and Finite-Size Effects

“…However, we have checked that the results remain qualitatively unchanged even if we include corrections arising from such fluctuations [42]. We stress that we aim at an understanding of the deviation of ξ from its value in the thermodynamic limit.…”

“…Note that the particle number is determined by the quantity k F L, where k F is the Fermi momentum. For details, we refer the reader to see [42] (color figure online) a spontaneous breakdown of the U(1) symmetry of the theory. In the following we will not give all the details of our finite-volume study which can be found in [42].…”

Improved lattice operators for nonrelativistic fermions

“…Eq. (13)]. The extension to the larger domain should be done respecting the periodicity of the momentum lattice.…”

“…[10] for the Hubbard model using dynamical mean-field theory, careful systematic studies in full-fledged MC calculations have only recently started to appear [4,5,11,12] and are still restricted to the ground state. Interestingly, recent studies based on functional renormalization group techniques [13] have also started to tackle the problem of extrapolating to infinite volume and particle number in the unitary limit.…”