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, γ(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 γ(T ) − γ(0) ∝ 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 γ and those in spin susceptibilities.

Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

“…We implement our approach in Fermi liquids, but it goes far beyond the standard Fermi liquid (FL) approach [10,11] that only fixes the first correction to the T = 0 linear regime. In contrast to what happens at higher dimensions, [34,35] we find that higher corrections remain analytic.…”

“…We implement our approach in Fermi liquids, but it goes far beyond the standard Fermi liquid (FL) approach [10,11] that only fixes the first correction to the T = 0 linear regime. In contrast to what happens at higher dimensions, [34,35] we find that higher corrections remain analytic.We proceed in three steps: First, the forcing out of equilibrium (that can be dynamical) is exactly incorporated in the description of the SC-FP for arbitrary QIM: we give explicitly the out-of-equilibrium density matrix.Second, we focus on integrable QIM and carry on a Keldysh expansion in the distance to the SC-FP. In the case of a super Fermi liquid in which only transfer of integer charges (in however complex processes) are allowed, analytical properties allow for an exact expression for the out-of-equilibrium average value of local operatorŝ A(x, t) in terms of equilibrium average value of effective operators in a free theory H sc 0 :…”

Nonanalytic magnetic response of Fermi and non-Fermi liquids

“…(6) and neglect the self-energy renormalization for a moment. Evaluating the derivatives of Ξ(T, H) with respect to T and H, we find that the prefactor of the T term in the specific heat coefficient diverges [9], whereas the prefactor of the |H| term in the spin susceptibility remains finite:…”

“…A linear increase of χ s with magnetization (and thus H) has been observed in a 2D GaAs heterostructure [8]. Since none of these experiments correspond to the weakcoupling limit, there is obviously a need for a nonperturbative treatment of nonanalytic terms.It has recently been shown [4,9] that the second-order result for γ(T, 0) in Eq. (1) becomes exact once the weakcoupling backscattering amplitudes Γ c,s (π) are replaced by the exact ones.…”

Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order

“…We now turn to the diagrams C and D. Using constraints (3.29) for the interaction vertices and (3.25) for the current vertices but keeping the momentum dependence of the Z-factors, we obtain for the sum of the diagrams C and D 36) [In deriving this result, we also used properties (3.17) and (3.22).] In general, Eq.…”