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arXiv:cond-mat/0302042 · Physical review. B, Condensed matter

Finite-energy Landau liquid theory for the one-dimensional Hubbard model: Pseudoparticle energy bands and degree of localization/delocalization

J. M. P. Carmelo, Pedro D Sacramento

Published Aug 13, 2003• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.68.085104

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Physical review. B, Condensed matter•Dec 1, 1992•33 citations
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.
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.
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.
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 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.
Abstract. 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 M th upper-Hubbard band lower limit. Here 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 U. 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. PACS numbers: 71.10.Fd, 64.60.Fr, 11.30.-j, 71.10.PmOne and Two-Electron Spectral Function Expressions... 2 1.
We use the Landau-liquid character of the low-energy eigenstate spectrum of the Hubbard chain in a magnetic field to investigate its two-particle spectral properties. The picture that emerges is that of a gas of two coupled fluids of pseudoparticles. The kinetic equations that govern the flow of pseudoparticles are derived. The macroscopic currents are expressed in terms of the elementary pseudoparticle currents. As a central result we evaluate in the limit of zero momentum the wave function for the electronic excitations obtained by applying the up-spin and down-spin density-fluctuation operators on the ground state. This wave function is calculated on the basis of the pseudoparticle single-pair eigenstates. It is defined by the microscopic two-particle matrix elements of the corresponding fluctuations taken between the ground state and the elementary excitations. The on-site interaction U, electronic density n, and magnetic field H dependence of these matrix elements, which play a major role in the two-particle spectral functions, provide relevant information on the microscopic foundation of the one-dimensional Landau-liquid theory. This leads to the introduction of an adiabatic continuity principle, which is valid in the Hilbert subspace of the pseudoparticle single-pair eigenstates of lowest energy and momentum. The non-Landau-liquid character of the zero-magnetic-field L\"uttinger phase, where such an adiabatic continuity principle is not valid, is explained.Exact expressions for the two-pseudoparticle forward-scattering amplitudes and for the charge-charge and spin-spin correlation functions at small momentum and low frequency are obtained. The dependence of the charge and spin stiffnesses of the conductivity spectra on U, n, and H, which is determined by the pseudoparticle transport masses, is investigated in detail. The study of these masses and of the effective charge and spin projection of the pseudoparticles gives information on their structure in the electronic representation. It is shown that the decoupling that characterizes the low-energy excitation spectrum does not correspond in the case of finite magnetic fields to a real charge-spin separation. Our results provide a method for the study of the low-frequency dynamics of interacting systems solvable with the Bethe ansatz, and we identify the spectral parameters that control the nonclassical critical exponents with microscopic two-electron matrix elements.