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arXiv:cond-mat/0305347

Description of the Energy Eigenstates of the 1D Hubbard Model in Terms of Rotated-Electron Site Distribution Configurations

J. M. P. Carmelo

Published May 15, 2003• 0 citations
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Abstract

In this paper we describe the pseudoparticles, holons, and spinons whose occupancy configurations describe the energy eigenstates of the one-dimensional (1D) Hubbard model in terms of rotated electrons. Rotated electrons are related to electrons by a mere unitary transformation such that rotated electron double occupation is a good quantum number. Moreover, we introduce the concepts of local pseudoparticle and effective pseudoparticle lattice. Our findings provide useful information about the relation of the exotic pseudoparticles, holons, and spinons that diagonalize the non-perturbative many-electron problem to the original electrons. We provide an example showing how the derived local pseudoparticle representation can be used in the evaluation of finite-energy few-electron spectral function expressions.

DOI
10.48550/arxiv.cond-mat/0305347

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In this paper we describe the pseudoparticles, holons, and spinons whose occupancy configurations describe the energy eigenstates of the one-dimensional (1D) Hubbard model in terms of rotated electrons. Rotated electrons are related to electrons by a mere unitary transformation such that rotated electron double occupation is a good quantum number. Moreover, we introduce the concepts of local pseudoparticle and effective pseudoparticle lattice. Our findings provide useful information about the relation of the exotic pseudoparticles, holons, and spinons that diagonalize the non-perturbative many-electron problem to the original electrons. We provide an example showing how the derived local pseudoparticle representation can be used in the evaluation of finite-energy few-electron spectral function expressions.
In the first paper of this series it was found that the ηηη-spin 1/2 holons, spin 1/2 spinons, and ccc pseudoparticles whose occupancy configurations describe the energy eigenstates of the one-dimensional Hubbard model emerge from the electron - rotated-electron unitary transformation. In this second paper we discuss and clarify how the relation of the electrons to the above objects can be used in a program for evaluation of finite-energy few-electron spectral functions. As a first step, here we characterize the dominant holon and spinon microscopic physical processes that originate more than 99% of the few-electron spectral weight. These dominant processes are related to exact selection rules for the values of the number of holons and spinons generated or annihilated by application onto a ground state of rotated-electron operators. We also generalize the concepts of a lower Hubbard band and upper Hubbard bands to all values of on-site Coulombian repulsion.
The relation of the rotated-electron site distribution configurations that describe the energy eigenstates of the one-dimensional Hubbard model to the momentum occupancy configurations of the same states associated with the Bethe ansatz quantum numbers is clarified. Our study involves the introduction of the concepts of a local pseudoparticle and an effective pseudoparticle lattice, needed for the relation of both the local pseudoparticle internal structure and the pseudoparticle occupancy configurations to the rotated-electron site distribution configurations. Our results provide further useful information about the microscopic mechanisms behind the anomalous finite-energy spectral properties of low-dimensional complex materials.
In this paper we consider the one-dimensional Hubbard model and study the deviations from the ground-state values of double occupation which result from creation or annihilation of holons, spinons, and pseudoparticles. These quantum objects are such that all energy eigenstates are described by their occupancy configurations. The band-momentum dependence of the obtained double-occupation spectra provides important information on the degree of localization/delocalization of the real-space lattice electron site distribution configurations associated with the pseudoparticles. We also study the band momentum, on-site electronic repulsion, and electronic density dependence of the pseudoparticle energy bands. The shape of these bands plays an important role in the finite-energy spectral properties of the model. Such a shape defines the form of the lines in the momentum-energy/frequency plane where the peaks and edges of the one-electron and two-electron spectral weight of physical operators are located. Our findings are useful for the study of the one-electron and two-electron spectral-weight distribution of physical operators.
Exotic elementary objects such as "holons" and "spinons", which are widely used in descriptions of correlated electrons in reduced spatial dimensions, were introduced from analysis of the excitation branches of one-dimensional (1D) models. The 1D Hubbard model with effective nearest-neighbor hopping integral t and on-site repulsion U is a prominent example. In the last twenty years a large number of angle-resolved photoemission spectroscopy experiments as well as electron energy-loss spectroscopic studies and high-resolution resonant inelastic X-ray experiments on several quasi-1D metals and quasi-1D Mott-Hubbard insulators have observed separate charge and spin spectral features, which have been identified with "holons" and "spinons". The elementary objects emerging within non-perturbative 1D correlated systems play now the same role in actual low-dimensional materials as Fermi-liquid quasiparticles in three-dimensional metals. The main goal of this paper is the review of representations of the 1D Hubbard model physics in terms of elementary objects whose configurations generate the energy eigenstates from the electron or hole vacuum. In addition, the relation to the holon and spinon representations is discussed and clarified.
In this paper we derive general expressions for few-electron spectral functions of the one-dimensional Hubbard model for values of the excitation energy in the vicinity of the MthM^{th}Mth upper-Hubbard band lower limit. Here M=1,2,...M=1,2,...M=1,2,... is the rotated-electron double occupation, which vanishes for the ground state and is a good quantum number for all values of the on-site Coulomb repulsion UUU. Our studies rely on a combination of symmetries of the model with a recent finite-energy holon and spinon description of the quantum problem. We apply our general scheme to the one-electron addition spectral function, dynamical structure factor, and spin singlet Cooper pair addition spectral function. Our results provide physically interesting information about the finite-energy spectral properties of the many-electron one-dimensional quantum liquid.
In this paper the spin configurations of the ground state and one- and two-electron excited states of the Hubbard model on the square lattice are studied. We profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U(1)SO(3)\times SO(3)\times U(1)SO(3)×SO(3)×U(1) symmetry. For rotated electrons, doubly and single occupancy are good quantum numbers for on-site repulsion U>0U>0U>0. The above states are within that description generated by occupancy configurations of charge ccc fermions and spin-singlet two-spinon s1s1s1 bond particles. Those describe the charge and spin degrees of freedom, respectively, of the rotated electrons that singly occupy sites. While the ccc fermions have no internal structure, that of the spin-neutral s1s1s1 bond-particle occupancy configurations is here described in terms of spinon occupancies of a well-defined effective spin lattice. In reference \cite{companion} it is confirmed that our results contribute to the further understanding of the role of electronic correlations in the spin spectrum of the parent compound La2_22​CuO4_44​. They are also of interest for studies of ultra-cold fermionic atoms on an optical lattice.