The Low-Energy Limiting Behavior of the Pseudofermion Dynamical Theory

Abstract

In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga-Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga-Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase