The dynamical correlation functions in one-dimensional electronic systems show power-law behaviour at low energies and momenta close to integer multiples of the charge and spin Fermi momenta. These systems are usually referred to as Tomonaga–Luttinger liquids. However, near well defined lines of the (k,ω) plane the power-law behaviour extends beyond the low-energy cases mentioned above, and also appears at higher energies, leading to singular features in the photoemission spectra and other dynamical correlation functions. The general spectral-function expressions derived in this paper were used in recent theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene–tetracyanoquinodimethane (TTF-TCNQ) metallic phase. They are based on a so-called pseudofermion dynamical theory (PDT), which allows us to systematically enumerate and describe the excitations in the Hubbard model starting from the Bethe ansatz, as well as to calculate the charge and spin object phase shifts appearing as 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 to half filling. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. In addition, the specific processes involved in the spectral features of TTF-TCNQ are studied. 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.

We review developments concerning the effect of correlations on the electronic properties of one-dimensional systems, focusing our analysis on the one-dimensional Hubbard model. We consider methods used to describe the exotic properties of these systems, ranging from bosonization associated with the Tomonaga and Luttinger liquid behavior, to the Bethe ansatz solution, referring to all energy scales of solvable quantum problems and the pseudoparticle description. We use that description to study the model energy spectrum and the low-energy quantities. In the ensuing companion chapter we discuss the relation of the electronic operators to these quantum objects.

This chapter follows its companion, chapter 1. Here we review different methods based on the Bethe ansatz solution of the one-dimensional Hubbard model, in order to study quantities related to charge transport and the momentum dependent conductivity. Moreover, we report recent developments on finite-energy dynamical properties. This is achieved by introducing new entities called pseudofermions which are basically free, in the sense that their energies are additive, and where the effect of the interactions appears through phase shifts that are absorbed by their discrete momentum values. The resulting pseudofermion dynamical theory enables the evaluation of matrix elements between energy eigen-states and hence the derivation of finite energy expressions for the one- and two-electron correlation and spectral functions. Comparison with experimental results is also discussed.

A dynamical theory which accounts for all microscopic one-electron processes is used to study the spectral function of the 1D Hubbard model for the whole (k,ω)-plane, beyond previous studies which focused on the weight distribution in the vicinity of the singular branch lines only. While our predictions agree with those of the latter studies concerning the tetracyanoquinodimethane (TCNQ) related singular features in photoemission of the organic compound tetrathiafulvalene–tetracyanoquinodimethane (TTF–TCNQ) metallic phase, the generalized theory also leads to quantitative agreement concerning the tetrathiafulvalene (TTF) related finite-energy spectral features, which are found to correspond to a value of the on-site repulsion U larger than for TCNQ. Our study reveals the microscopic mechanisms behind the unusual spectral features of TTF–TCNQ and provides a good overall description of those features for the whole (k,ω)-plane.

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.

We derive general closed-form analytical expressions for the finite-energy one- and two-electron spectral-weight distributions of an one-dimensional correlated metal with on-site electronic repulsion. Our results also provide general expressions for the one- and two-atom spectral functions of a correlated quantum system of cold fermionic atoms in a one-dimensional optical lattice with onsite atomic repulsion. In the limit of zero spin density our spectral-function expressions provide the correct zero-spin density results. Our results reveal the dominant non-perturbative microscopic many-particle mechanisms behind the exotic spectral properties observed in quasi-one-dimensional metals and correlated systems of cold fermionic atoms in one-dimensional optical lattices. (c) 2005 Elsevier B.V. All rights reserved.

We discuss the magnetic phases of the Hubbard model for the honeycomb lattice both in two and three spatial dimensions. A ground state phase diagram is obtained depending on the interaction strength U and electronic density n. We find a first order phase transition between ferromagnetic regions where the spin is maximally polarized (Nagaoka ferromagnetism) and regions with smaller magnetization (weak ferromagnetism). When taking into account the possibility of spiral states, we find that the lowest critical U is obtained for an ordering momentum different from zero. The evolution of the ordering momentum with doping is discussed. The magnetic excitations (spin waves) in the antiferromagnetic insulating phase are calculated from the random-phase approximation for the spin susceptibility. We also compute the spin fluctuation correction to the mean field magnetization by virtual emission/absorption of spin waves. In the large U limit, the renormalized magnetization agrees qualitatively with the Holstein-Primakoff theory of the Heisenberg antiferromagnet, although the latter approach produces a larger renormalization.