Excitation spectrum of the one-dimensional Fermi gas with backward scattering

The energy spectrum of the one-dimensional electron gas, solved by Luther and Emery for a particular attractive interaction strength $U$ of the backward scattering across the Fermi surface, has been calculated for small deviations from this particular limit. The energy spectrum shows a gap at the Fermi energy, whose magnitude is very sensitive to the interaction $U$. The density of states shows a gap at zero temperature, which is smeared out by the quasiparticle lifetime for $T\ne 0$.