Correlation-function asymptotic expansions: pre-factors universality

TL;DR

This paper demonstrates the universality of pre-factors in the asymptotic expansions of correlation functions in the 1D Hubbard model, linking low-energy behavior to scattering mechanisms and broadening understanding of quasi-1D systems.

Contribution

It calculates universal pre-factors for correlation-function asymptotics and clarifies their relation to scattering mechanisms across energy scales.

Findings

Pre-factors of correlation-function terms are universal.

Low-energy behavior relates to scattering mechanisms.

Results apply broadly to integrable models and nanostructures.

Abstract

We show that the pre-factors of all terms of the one-dimensional Hubbard model correlation-function asymptotic expansions have an universal form, as the corresponding critical exponents. In addition to calculating such pre-factors, 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.