Scaling limit of the one-dimensional attractive Hubbard model: the non-half-filled band case Original Research Article

The scaling limit of the less than half-filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0 < n < 1) while adjusting the interaction and bandwidth in such a way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find that similarly to the half-filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half-filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half-filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c = 1 and SU(2) × SU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half-filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory.