Low energy excitations and singular contributions in the thermodynamics of clean Fermi liquids

Abstract

Using a recently suggested method of bosonization in an arbitrary dimension, we study the anomalous contribution of the low energy spin and charge excitations to thermodynamic quantities of a two-dimensional (2D) Fermi liquid. The method is slightly modified for the present purpose such that the effective supersymmetric action no longer contains the high energy degrees of freedom but still accounts for effects of the finite curvature of the Fermi surface. Calculating the anomalous contribution $\delta c(T)$ to the specific heat, we show that the leading logarithmic in temperature corrections to $\delta c(T)/T^2$ can be obtained in a scheme combining a summation of ladder diagrams and renormalization group equations. The final result is represented as the sum of two separate terms that can be interpreted as coming from singlet and triplet superconducting excitations. The latter may diverge in certain regions of the coupling constants, which should correspond to the formation of triplet Cooper pairs.

29 pages, 13 figures

References in corpus (8)

• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• Temperature dependence of spin susceptibility in two-dimensional Fermi liquid systems
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Specific heat of a one-dimensional interacting Fermi system: the role of anomalies

Cited by in corpus (7)

• First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
• Strongly correlated two-dimensional plasma explored from entropy measurements
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Effective Soft-Mode Theory of Strongly Interacting Fermions
• Nonanalyticities in a Strongly Correlated Fermi Liquid: Corrections to Scaling at the Fermi-Liquid Fixed Point
• Dimensional reduction of the Luttinger-Ward functional for spin-degenerate $D$-dimensional electron gases
• Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals