Strongly interacting Luttinger liquid-exact solution of a generalized t-J model in one dimension

Luttinger liquids are characterized by the critical exponent Θ of the momentum distribution around the Fermi momentum k_F. Typically Θ le; 1/2, signalling a singularity characterizing a residual Fermi surface. Results of photoemission experiments can be interpreted in terms strongly interacting Luttinger liquids with Θ ≥ 1 with the residual Fermi surface disappearing. We construct integrable models with such behaviour-models given by the SU(v) t-J interaction with a hard-core repulsive potential between electrons at distances less than or equal to Δ. The models exhibit both weakly and strongly interacting Luttinger behaviours with Θ varying continuously in the range 0 ≤ Θ ≤ 1/2 (1 + Δ - 1/[v(1 + Δ)])² depending on the electron density. In the extreme high-density limit the model exhibits a Mott-Hubbard gap and reduces to an isotropic Heisenberg chain with a new spacing parameter Δ + 1.