Article,
Nonanalytic corrections to the Fermi liquid behavior
Phys. Rev. B, (2003)
DOI: 10.1103/PhysRevB.68.155113
Abstract
The issue of nonanalytic corrections to the Fermi-liquid behavior
is revisited. Previous studies have indicated that the corrections
to the Fermi-liquid forms of the specific heat and the static spin
susceptibility (CFL∝T,χsFL=const) are nonanalytic in D<~3 and scale
as δC(T)∝TD, χs(T)∝TD-1, and χs(Q)∝QD-1, with extra logarithms in
D=3 and 1. It is shown that these nonanalytic corrections originate
from the universal singularities in the dynamical bosonic response
functions of a generic Fermi liquid. In contrast to the leading,
Fermi-liquid forms which depend on the interaction averaged over
the Fermi surface, the nonanalytic corrections are parametrized by
only two coupling constants, which are the components of the interaction
potential at momentum transfers q=0 and q=2pF. For three-dimensional
(3D) systems, a recent result of Belitz, Kirkpatrick, and Vojta for
the spin susceptibility is reproduced and the issue why a nonanalytic
momentum dependence, χs(Q,T=0)-χsFL∝Q2logQ, is not paralleled by
a nonanalyticity in the T dependence χs(0,T)-χsFL∝T2 is clarified.
For 2D systems, explicit forms of C(T)-CFL∝T2, χ(Q,T=0)-χFL∝|Q|,
and χ(0,T)-χFL∝T are obtained. It is shown that earlier calculations
of the temperature dependences in two dimensions are incomplete.
