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 angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.
We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.
This pre-print deals with the one dimensional Hubbard model, as described by the Pseudofermion Dynamical Theory (PDT), with the purpose of (1) deriving a novel expression for the one electron spectral function for all values of the on-site repulsion
U/t and filling
n∈(0,1), at vanishing magnetisation
m→0, and (2) discover how to correctly compare the results originating from two different theoretical frameworks in the
U/t→∞ limit, as a first-test of the novel expressions obtained in this paper. Thus, an exact expression of the spectral function is obtained, which is furthermore successfully compared with previously known results in the
U→∞ limit. Following the PDT, the expression for the one electron spectral function factorises into a spin part and a charge part for all values of the on-site repulsion
U/t, where the dynamical quantum objects are spin zero and
η-spin (charge) zero singlet pairs of so-called rotated electrons, which in turn are obtained from the original electrons by a unitary transformation. The spectral function is exemplified for
U/t=400, with the purpose of comparing it with the same function obtained by other authors (and other means) in the
U→∞ limit. The main pillars of the PDT is presented in a summarised form. For example, we will only be interested in excited energy eigenstates which originate the most significant singular features of the spectral map in the
(k,ω) plane, safely ignoring higher order contributions. Even though emphasis is given on step-by-step derivations where necessary, derivations that have been done elsewhere and/or do not notably contribute to the physical understanding, are sometimes avoided. Therefore, references for further study are given throughout the paper.
The momentum, electronic density, spin density, and interaction dependences of the exponents that control the ( k , ω ) -plane singular features of the σ = ↑ , ↓ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined in terms of the rotated electrons associated with the model Bethe-ansatz solution for all electronic density and spin density values and the whole finite repulsion range. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the one-electron matrix elements between the ground state and excited energy eigenstates.
This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin and spin zero objects, and are the scatterers and the scattering centers of the theory. The S-matrix of this representation is a simple phase factor, involving the phase shifts of the zero energy forward momentum scattering events. A PF dynamical theory is developed and applied to the one-electron removal and lower Hubbard band addition cases. For any value of the on-site effective Coloumb repulsion and electronic density, and in the limit of zero magnetization, we derive closed form expressions for these spectral functions, showing the emergence of the power-law type behavior of correlation functions of Luttinger liquids. However, our expressions are valid for the entire elementary excitation energy bandwidth. The singular behavior of the theoretical spectral weight leads to a spectral weight distribution detectable by photo emission and photo absorption experiments. As an important contribution to the understanding of quasi 1D materials, we are able to reproduce for the whole energy bandwidth, the experimental spectral distributions recently found for the organic compound TTF-TCNQ. This confirms the validity of the PF dynamical theory, and provides a deeper understanding of low dimensional correlated systems.
In one-dimensional (1D) non-perturbative many-electron problems such as the 1D Hubbard model the electronic charge and spin degrees of freedom separate into exotic quantum objects. However, there are two different representations for such objects and associated scattering quantities whose relation is not well understood. Here we solve the problem by finding important information about the relation between the corresponding alternative choices for one-particle scattering states. Our study reveals why one of these representations, the {\it pseudofermion} representation, is the most suitable for the description of the unusual finite-energy spectral and dynamical properties of the model. This is a problem of physical importance, since the exotic independent charge and spin finite-energy spectral features observed by angle-resolved photoelectron spectroscopy in quasi-1D metals was found recently to correspond to the charge and spin quantum objects of the pseudofermion representation.