https://doi.org/10.1140/epjd/e2015-60597-1
Regular Article
Renormalization group analysis of ultracold Fermi gases with two-body attractive interaction
1 School of Science, Tianjin University
of Science and Technology, Tianjin
300457, P.R.
China
2 Department of Basic Courses, Tianjin
University of Finance and Economics Pearl River College, Tianjin
301811, P.R.
China
3 School of Mathematics and Computer
Science, Guizhou Normal University, Guizhou
550001, P.R.
China
4 School of Science, Tianjin University
of Technology and Education, Tianjin
300222, P.R.
China
a
e-mail: gxyauthor@tust.edu.cn
Received:
22
October
2015
Received in final form:
9
December
2015
Published online:
26
January
2016
We propose a new functional renormalization group (RG) strategy to investigate the many-body physics of interacting ultracold Fermi gases. By mapping the Ginzburg-Landau (GL) action of Fermi gases onto a complex φ4-model, we can obtain the closed flow equation in the one-loop approximation. An analysis of the emerging RG flow gives the ground state behavior. The Hamiltonian of a Fermi gas with a two-body attractive interaction is used as a demonstration to clarify our treatment. The fixed point structure reveals not only the condensation phase transition, but also the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. The effect of the imaginary time renormalization is also discussed. It is shown that for the dynamical field configuration our RG procedure can reproduce the well known theoretical results of BCS-BEC crossover, while under a static approximation the phase transition takes place at a higher critical temperature.
Key words: Cold Matter and Quantum Gas
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2016