Pairing in many-fermion systems: an exact renormalisation group treatment

We study the application of the exact renormalisation group to a many-fermion system with a short-range attractive force. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a set of approximate flow equations for the effective couplin...

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Bibliographic Details
Published inPhysics letters. B Vol. 605; no. 3-4; pp. 287 - 294
Main Authors Birse, Michael C., Krippa, Boris, McGovern, Judith A., Walet, Niels R.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 13.01.2005
Elsevier Science
Subjects
Exact sciences and technology
Physics
The physics of elementary particles and fields
Fluctuations
Critical value
Fermions
Attraction interaction
Phase transitions
Scattering lengths
Fermion systems
Initial conditions
Numerical solution
Short-range interactions
Boson field
Renormalization
Pairing
Renormalization group
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Summary:We study the application of the exact renormalisation group to a many-fermion system with a short-range attractive force. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The initial conditions are obtained by renormalising the interaction to fit the scattering length in vacuum. At some critical value of the running scale, the numerical solutions show a phase transition to a gapped phase. Standard results are recovered if we omit the boson loops. When boson fluctuations are included, we find that their contributions are significant only in the small-gap regime.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2004.11.044