Correlation-function asymptotic expansions: Universality of prefactors of the one-dimensional Hubbard model

We show that the prefactors of all terms of the one-dimensional (1D) Hubbard model correlation-function asymptotic expansions have a universal form, as the corresponding critical exponents. In addition to calculating such prefactors, our study clarifies the relation of the low-energy Tomonaga-Luttinger-liquid behavior to the scattering mechanisms which control the spectral properties of the model at all energy scales. Our results are of general nature for many integrable interacting models and provide a broader understanding of the unusual properties of quasi-1D nanostructures, organic conductors, and optical lattices of fermionic atoms.