Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions

I. L. Aleiner and K. B. Efetov
Phys. Rev. B 74, 075102 – Published 4 August 2006

Abstract

We suggest a method of calculations for a clean Fermi gas with a repulsion in any dimension. This method is based on writing equations for quasiclassical Green functions and reducing them to equations for collective spin and charge excitations. The spin excitations interact with each other, and this leads to nontrivial physics. Writing the solution of the equations and the partition function in terms of a functional integral over supervectors and averaging over fluctuating fields we come to an effective field theory describing the spin excitations. In some respects, the theory is similar to bosonization but also includes the “ghost” excitations, which prevents overcounting of the degrees of freedom. Expansion in the interaction reveals logarithmic in temperature corrections. This enables us to suggest a renormalization group scheme and derive renormalization group equations. Solving these equations and using their solutions for calculating thermodynamic quantities we obtain explicit expression for the specific heat containing only an effective amplitude of the backward scattering. This amplitude has a complicated dependence on the logarithm of temperature, which leads to a nontrivial temperature dependence of the specific heat.

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  • Received 14 February 2006

DOI:https://doi.org/10.1103/PhysRevB.74.075102

©2006 American Physical Society

Authors & Affiliations

I. L. Aleiner1 and K. B. Efetov2,3

  • 1Physics Department, Columbia University, New York, New York 10027, USA
  • 2Theoretische Physik III, Ruhr-Universität Bochum, 44780 Bochum, Germany
  • 3L. D. Landau Institute for Theoretical Physics, 117940 Moscow, Russia

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Issue

Vol. 74, Iss. 7 — 15 August 2006

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