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arXiv:cond-mat/9505029

Electrons, pseudoparticles, and quasiparticles in one-dimensional interacting electronic systems

J. M. P. Carmelo, A. H. Castro Neto, Nuno M. R. Peres

Published May 8, 1995• 0 citations
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Abstract

We find the singular transformation between the electron operator and the pseudoparticle operators for the Hubbard chain. We generalize the concept of quasiparticle to one-dimensional electronic systems which in 1D refers to many-pseudoparticle objects. We obtain explicit results for the electron renormalization factor, self energy, and vertex functions at the Fermi points. We also discuss the possible connection of our results to higher dimensions and explore the possibilities of instabilities in the interacting problem such as the formation of Cooper pairs.

DOI
10.48550/arxiv.cond-mat/9505029

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We find the singular transformation between the electron operator and the pseudoparticle operators for the Hubbard chain. We generalize the concept of quasiparticle to one-dimensional electronic systems which in 1D refers to many-pseudoparticle objects. We obtain explicit results for the electron renormalization factor, self energy, and vertex functions at the Fermi points. We also discuss the possible connection of our results to higher dimensions and explore the possibilities of instabilities in the interacting problem such as the formation of Cooper pairs.
We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The \ensuremath{\uparrow} and \ensuremath{\downarrow} quasiparticles recombine the pseudoparticle colors c and s (charge and spin at zero-magnetic field) and are constituted by one many-pseudoparticle topological-momentum shift and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron-quasiparticle transformation has a singular character which justifies the perturbative and nonperturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron-quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests their existence in quantum liquids in dimensions 1D3. However, whether the electron-quasiparticle overlap can vanish in D>1 or whether it becomes finite as soon as we leave 1D remains an unsolved question. \textcopyright{} 1996 The American Physical Society.
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 authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.
The authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.
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.
We introduce an operator algebra for the description of the low-energy physics of one-dimensional, integrable, multicomponent quantum liquids. Considering the particular case of the Hubbard chain in a magnetic field and chemical potential, we show that at low energy its Bethe-ansatz solution can be interpreted in terms of a pseudoparticle-operator algebra. Our algebraic approach provides a concise interpretation of, and justification for, several recent studies of low-energy excitations and trasnport which have been based on detailed analyses of specific Bethe-ansatz eigenfunctions and eigenenergies. A central point is that the exact ground state of the interacting many-electron problem is the noninteracting pseudoparticle ground state. Furthermore, in the pseudoparticle basis, the quantum problem becomes perturbative, i.e., the two-pseudoparticle forward-scattering vertices and amplitudes do not diverge, and one can define a many-pseudoparticle perturbation theory. We write the general quantum-liquid Hamiltonian in the pseudoparticle basis and show that the pseudoparticle-perturbation theory leads, in a natural way, to the generalized Landau-liquid approach.