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Journal of Physics C Solid State Physics

Low-energy excited states in a Hubbard chain with on-site attraction

Ferenc Woynarovich

Published Dec 10, 1983• 86 citations
Publisher

Abstract

The structure and energy of the eigenstates of a 1D Hubbard Hamiltonian with negative U is studied. Solutions for the Lieb-Wu equations (1968) corresponding to U<0 are constructed from those for U>0. It is found that the ground state is continuous, while the ground-state energy, although continuous, is not analytic at the U=0 point. In the excited states, in contrast to the U>0 case, both kinds of excitation are connected with the charge distribution and the state of the spins does not affect the energy explicitly. It is also found that the distribution of parameters can change discontinuously in the excited states as U crosses zero.

DOI
10.1088/0022-3719/16/34/009

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Journal of Physics C Solid State Physics•Jan 10, 1982•64 citations
The structure and energy of the eigenstates of a 1D Hubbard Hamiltonian with negative U is studied. Solutions for the Lieb-Wu equations (1968) corresponding to U<0 are constructed from those for U>0. It is found that the ground state is continuous, while the ground-state energy, although continuous, is not analytic at the U=0 point. In the excited states, in contrast to the U>0 case, both kinds of excitation are connected with the charge distribution and the state of the spins does not affect the energy explicitly. It is also found that the distribution of parameters can change discontinuously in the excited states as U crosses zero.
The structure and energy of the eigenstates of a 1D Hubbard Hamiltonian with negative U is studied. Solutions for the Lieb-Wu equations (1968) corresponding to U 0. It is found that the ground state is continuous, while the ground-state energy, although continuous, is not analytic at the U=0 point. In the excited states, in contrast to the U>0 case, both kinds of excitation are connected with the charge distribution and the state of the spins does not affect the energy explicitly. It is also found that the distribution of parameters can change discontinuously in the excited states as U crosses zero.
Those excited states of a half-filled 1D Hubbard chain that are connected with electron pairs occupying the same site are studied. It is argued that these states should be described by solutions of the Lieb-Wu equations (1968) in which some of the wavenumbers are complex. Solutions of this type have been found that correspond to states in which the spin part is not excited. The energy-momentum dispersion is also calculated. The gap in the spectrum of the single excitations equals the discontinuity of the chemical potential calculated by Lieb and Wu.
The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.