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arXiv:1407.5438 · Physics Letters B

Pairing in asymmetric many-fermion systems: Functional renormalisation group approach

Boris Krippa

Published Apr 6, 2015• 12 citations
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Abstract

Functional renormalisation group approach is applied to a imbalanced many-fermion system with a short-range attractive force. We introduce a composite boson field to describe pairing effects, and assume a simple ansatz for the effective action. A set of approximate flow equations for the effective coupling including boson and fermionic fluctuations is derived and solved. We identify the critical values of particle number density mismatch when the system undergoes a normal state. We determine the phase diagram both at unitarity and around. The obtained phase diagram is in a reasonable agreement with the experimental data.

DOI
10.1016/j.physletb.2015.03.057

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Functional renormalisation group approach is applied to a imbalanced many-fermion system with a short-range attractive force. We introduce a composite boson field to describe pairing effects, and assume a simple ansatz for the effective action. A set of approximate flow equations for the effective coupling including boson and fermionic fluctuations is derived and solved. We identify the critical values of particle number density mismatch when the system undergoes a normal state. We determine the phase diagram both at unitarity and around. The obtained phase diagram is in a reasonable agreement with the experimental data.
The application of the exact renormalisation group to symmetric as well as asymmetric many-fermion systems with a short-range attractive force is studied. Assuming an ansatz for the effective action with effective bosons, describing pairing effects a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations has been derived. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator are shown to lead to a similar results. We find that, being quite small in the case of the symmetric many-fermion system the corrections to mean field approximation becomes more important with increasing mass asymmetry.
The application of the exact renormalization group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator were shown to lead to similar results.
We consider pairing phenomena in the framework of the exact renormalization group. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a set of approx. flow equations for the effective coupling including boson and fermionic fluctuations. The initial conditions are obtained by renormalizing the interaction to fit the scattering length in vacuum. At some crit. value of the running scale, the numerical solns. show a phase transition to a gapped phase. Std. results are recovered if we omit the boson loops. [on SciFinder (R)]
We study the exact renormalization group flow for ultracold Fermi gases in the unitary regime. We introduce a pairing field to describe the formation of the Cooper pairs and take a simple ansatz for the effective action. A set of approximate flow equations for effective couplings including boson and fermionic fluctuations is derived. At some value of the running scale, the system undergoes a phase transition to a gapped phase. The values of the energy density, chemical potential, pairing gap and the corresponding proportionality constants relating the interacting and non-interacting Fermi gases are calculated. Standard mean-field results are recovered if we omit the boson loops.