Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid

Abstract

We revisit the issue of the leading nonanalytic corrections to the temperature dependence of the specific heat coefficient, $\gamma (T)=C(T)/T,$ for a system of interacting fermions in three dimensions. We show that the leading temperature dependence of the specific heat coefficient $\gamma (T)-\gamma (0)\propto T^3\ln T$ comes from two physically distinct processes. The first process involves a thermal excitation of a single particle-hole pair, whose components interact via a nonanalytic dynamic vertex. The second process involves an excitation of three particle-hole pairs which interact via the analytic static fixed-point vertex. We show that the single-pair contribution is expressed via the backscattering amplitude of quasiparticles at the Fermi surface. The three-pair contribution does not have a simple expression in terms of scattering in particular directions. We clarify the relation between these results and previous literature on both 3D and 2D systems, and discuss the relation between the nonanalyticities in $\gamma$ and those in spin susceptibilities.

References in corpus (16)

• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Bosonization and Fermion Liquids in Dimensions Greater Than One
• Quantum-critical behavior of itinerant ferromagnets
• Bosonization of the Low Energy Excitations of Fermi Liquids
• Non-analytic corrections to the Fermi-liquid behavior
• Bosonization of Fermi liquids
• Interaction corrections to the thermal transport coefficients in disordered metals: quantum kinetic equation approach
• Singular perturbation theory for interacting fermions in two dimensions
• Non-Analytic Contributions to the Self-Energy and the Thermodynamics of Two-Dimensional Fermi Liquids
• Universal corrections to the Fermi-liquid theory
• The First Temperature Corrections to the Fermi Liquid Fixed Point in Two Dimensions
• Leading Temperature Corrections to Fermi Liquid Theory in Two Dimensions
• Universal temperature corrections to Fermi liquid theory in an interacting electron system
• Thermodynamics of a Fermi liquid beyond the low-energy limit
• Interacting fermions in two dimensions: beyond the perturbation theory
• Temperature dependent spin susceptibility in a two-dimensional metal

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