Free energy and excitation spectrum of a one-dimensional fermi system

Abstract

The free energy of a 1-d system of spin 1/2 fermions is studied by means of a perturbation expansion with respect to the spin-flip backward scattering (q ≈ 2k F ) part of the interaction. The perturbation series is analyzed by comparing it with the free energy of a noninteracting quasi fermion system which is characterized by the spectrume F ± [Δ δ +(υ∥k|−k F |) δ ]1/δ . The connection between the parametersΔ andδ and the coupling constants of the original fermion system is established. A gap in the spin-excitation spectrum is found to exist atT=0 only. The absence of such a gap at finite temperatures is in agreement with the absence of long range order atT ≠ 0.