Dynamical functions of a 1D correlated quantum liquid

Abstract

The dynamical correlation functions in one-dimensional electronic systems showpower-law behaviour at low energies and momenta close to integer multiplesof the charge and spin Fermi momenta. These systems are usually referredto as Tomonaga–Luttinger liquids. However, near well defined lines of the(k,ω) plane the power-law behaviour extends beyond the low-energy cases mentionedabove, and also appears at higher energies, leading to singular features in thephotoemission spectra and other dynamical correlation functions. The generalspectral-function expressions derived in this paper were used in recent theoretical studies ofthe finite-energy singular features in photoemission of the organic compoundtetrathiafulvalene–tetracyanoquinodimethane (TTF-TCNQ) metallic phase. They arebased on a so-called pseudofermion dynamical theory (PDT), which allows us tosystematically enumerate and describe the excitations in the Hubbard model starting fromthe Bethe ansatz, as well as to calculate the charge and spin object phase shifts appearingas exponents of the power laws. In particular, we concentrate on the spin-density limit and on effects in the vicinity of the singular border lines, as well as close tohalf filling. Our studies take into account spectral contributions from types ofmicroscopic processes that do not occur for finite values of the spin density. Inaddition, the specific processes involved in the spectral features of TTF-TCNQ arestudied. Our results are useful for the further understanding of the unusual spectralproperties observed in low-dimensional organic metals and also provide expressionsfor the one- and two-atom spectral functions of a correlated quantum system ofultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.