Nonanalytic corrections to the Fermi-liquid behavior

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 ${(C}^{\mathrm{FL}}\ensuremath{\propto}T,{\ensuremath{\chi}}_{s}^{\mathrm{FL}}=\mathrm{const})$ are nonanalytic in $D<~3$ and scale as $\ensuremath{\delta}C(T)\ensuremath{\propto}{T}^{D},$ ${\ensuremath{\chi}}_{s}(T)\ensuremath{\propto}{T}^{D\ensuremath{-}1},$ and ${\ensuremath{\chi}}_{s}(Q)\ensuremath{\propto}{Q}^{D\ensuremath{-}1},$ 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 ${q=2p}_{F}.$ 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, ${\ensuremath{\chi}}_{s}(Q,T=0)\ensuremath{-}{\ensuremath{\chi}}_{s}^{\mathrm{FL}}\ensuremath{\propto}{Q}^{2}\mathrm{log}Q,$ is not paralleled by a nonanalyticity in the T dependence $[{\ensuremath{\chi}}_{s}(0,T)\ensuremath{-}{\ensuremath{\chi}}_{s}^{\mathrm{FL}}]\ensuremath{\propto}{T}^{2}$ is clarified. For 2D systems, explicit forms of $C(T)\ensuremath{-}{C}^{\mathrm{FL}}\ensuremath{\propto}{T}^{2},$ $\ensuremath{\chi}(Q,T=0)\ensuremath{-}{\ensuremath{\chi}}^{\mathrm{FL}}\ensuremath{\propto}|Q|,$ and $\ensuremath{\chi}(0,T)\ensuremath{-}{\ensuremath{\chi}}^{\mathrm{FL}}\ensuremath{\propto}T$ are obtained. It is shown that earlier calculations of the temperature dependences in two dimensions are incomplete.