Finite Energy Electronic Correlations in Low-Dimensional Systems

TL;DR

This thesis develops a dynamical theory for the 1D Hubbard model using PseudoFermions, deriving spectral functions that explain experimental observations in low-dimensional materials like TTF-TCNQ.

Contribution

It introduces a PseudoFermion-based dynamical theory applicable across the entire energy bandwidth of the 1D Hubbard model, matching experimental spectral data.

Findings

Derived closed-form spectral functions valid for all energy scales.

Reproduced experimental spectral distributions of TTF-TCNQ.

Confirmed the power-law behavior of correlation functions in Luttinger liquids.

Abstract

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.