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arXiv:nucl-th/0512083 · Journal of Physics A Mathematical and General

Superfluidity within exact renormalization group approach

Boris Krippa

Published Jun 7, 2006• 4 citations
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Abstract

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.

DOI
10.1088/0305-4470/39/25/s19

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We present a comprehensive analysis of quantum fluctuation effects in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The superfluid order parameter and fluctuations thereof are implemented by a bosonic Hubbard-Stratonovich field, which splits into two components corresponding to longitudinal and transverse (Goldstone) fluctuations. Physical properties of the system are computed from a set of approximate flow equations obtained by truncating the exact functional renormalization group flow of the coupled fermion-boson action. The equations capture the influence of fluctuations on nonuniversal quantities such as the fermionic gap, as well as the universal infrared asymptotics present in every fermionic superfluid. We solve the flow equations numerically in two dimensions and compute the asymptotic behavior analytically in two and three dimensions. The fermionic gap $\ensuremath{\Delta}$ is reduced significantly compared to the mean-field gap, and the bosonic order parameter $\ensuremath{\alpha}$, which is equivalent to $\ensuremath{\Delta}$ in mean-field theory, is suppressed to values below $\ensuremath{\Delta}$ by fluctuations. The fermion-boson vertex is only slightly renormalized. In the infrared regime, transverse order-parameter fluctuations associated with the Goldstone mode lead to a strong renormalization of longitudinal fluctuations: the longitudinal mass and the bosonic self-interaction vanish linearly as a function of the scale in two dimensions, and logarithmically in three dimensions, in agreement with the exact behavior of an interacting Bose gas.