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Keywords
(6)
Correlation Function
Fixed Point
Low Energy
Renormalization Group
Fermi Liquid
Long Wavelength
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The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid
The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid,10.1103/PhysRevB.82.195104,Physical Review B,S. A. Parameswaran,R.
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The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid
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S. A. Parameswaran
,
R. Shankar
,
S. L. Sondhi
A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a
Fermi liquid
and find that the answer is that it does {\it not}. From the perspective of the
renormalization group
for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the
Fermi liquid
fixed point
and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the
renormalization group
viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a CallanSymanzik equation for the repulsive
Fermi liquid
using the momentumshell renormalization group, and use it to compute the longwavelength behavior of the superconducting
correlation function
in the emergent lowenergy theory. We expect this technique to be of broader interest.
Journal:
Physical Review B  PHYS REV B
, 2010
DOI:
10.1103/PhysRevB.82.195104
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