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 spectrumε 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.
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Everts, H.U., Schulz, H. Free energy and excitation spectrum of a one-dimensional fermi system. Z Physik B 22, 285–294 (1975). https://doi.org/10.1007/BF01362252
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DOI: https://doi.org/10.1007/BF01362252