PACS. 71.10.Pm -Fermions in reduced dimensions. PACS. 71.27.+a -Strongly correlated electron systems.Abstract. -The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U . To achieve this goal we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angleresolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.The finite-energy spectral dispersions recently observed in quasi-one-dimensional (1D) metals by angle-resolved photoelectron spectroscopy (ARPES) reveal significant discrepancies from the conventional band-structure description [1,2]. The study of the microscopic mechanisms behind these unusual finite-energy spectral properties remains until now an interesting open problem. There is some evidence that the correlation effects described by the 1D Hubbard model might contain such finite-energy mechanisms [1,2]. However, for finite values of the on-site repulsion U very little is known about its finite-energy spectral properties, in contrast to simpler models [3]. Bosonization [4] and conformal-field theory [5] do not apply at finite energy. For U → ∞ the method of Ref.[6] provides valuable qualitative information, yet a quantitative description of the finite-energy spectral properties of quasi-1D metals requires the solution of the problem for finite values of U . The method of Ref. [7] refers to features of the insulator phase. For U ≈ 4t, where t is the transfer integral, there are numerical results for the one-electron spectral function [8] which, unfortunately, provide very little information about the microscopic mechanisms behind the finite-energy spectral properties. Recent preliminary results obtained by use of the finite-energy holon and spinon description introduced in Refs. [9-11] predict separate one-electron charge and spin spectral branch lines [1]. For the electron-removal spectral function these lines show quantitative agreement with the peak dispersions observed by ARPES in the quasi-1D organic conductor TTF-TCNQ [1]. However,

We study the electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ by means of density-functional band theory, Hubbard model calculations, and angle-resolved photoelectron spectroscopy ͑ARPES͒. The experimental spectra reveal significant quantitative and qualitative discrepancies to band theory. We demonstrate that the dispersive behavior as well as the temperature dependence of the spectra can be consistently explained by the finite-energy physics of the one-dimensional Hubbard model at metallic doping. The model description can even be made quantitative, if one accounts for an enhanced hopping integral at the surface, most likely caused by a relaxation of the topmost molecular layer. Within this interpretation the ARPES data provide spectroscopic evidence for the existence of spin-charge separation on an energy scale of the conduction bandwidth. The failure of the one-dimensional Hubbard model for the low-energy spectral behavior is attributed to interchain coupling and the additional effect of electron-phonon interaction.

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.