Novel few-body universality and many-body crossover physics

D. Blume

José Paulo D'Incao

Michael M. Scherer, Stefan Floerchinger, Holger Gies A

We review the functional renormalization group (RG) approach to the BCS-BEC crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

Lucas Platter

Yusuke Nishida, Dam Thanh Son

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich field of universal few-body and many-body physics in one dimension.

Spartak T. Belyaev