Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics C Solid State Physics

Excitations with complex wavenumbers in a Hubbard chain. II. States with several pairs of complex wavenumbers

Ferenc Woynarovich

Published Jan 10, 1982• 64 citations
Publisher

Abstract

For pt.I see ibid., vol.15, no.1, p.85 (1982). States of the 1D Hubbard chain with several pairs of complex wavenumbers are studied. The original set of Lieb-Wu equations (1968) is replaced by an equivalent set in which only real wavenumbers appear. These equations are reduced for the states in which the spin degrees of freedom are not excited. The energy-momentum dispersion for these states is also found.

DOI
10.1088/0022-3719/15/1/008

Related papers

Excitations with complex wavenumbers in a Hubbard chain. I. States with one pair of complex wavenumbers

Ferenc Woynarovich

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.

Journal of Physics C Solid State Physics•Jan 10, 1982•132 citations

Spin excitations in a Hubbard chain

Ferenc Woynarovich

The spin excitations of a Hubbard chain are calculated on the basis of the Lieb-Wu equations (1968). A system of equations, which contains the parameters of the excitation only, is derived. It is found that both the energy and the momentum of the spin excitations depend only on the positions of the holes in the real gamma distribution. The energy-momentum dispersion for a half-filled band is given. The structure and degeneracy of the lowest energy excitations are also discussed.

Journal of Physics C Solid State Physics•Sep 30, 1983•50 citations

Spin excitations in a Hubbard chain

Ferenc Woynarovich

The spin excitations of a Hubbard chain are calculated on the basis of the Lieb-Wu equations (1968). A system of equations, which contains the parameters of the excitation only, is derived. It is found that both the energy and the momentum of the spin excitations depend only on the positions of the holes in the real gamma distribution. The energy-momentum dispersion for a half-filled band is given. The structure and degeneracy of the lowest energy excitations are also discussed.

Advanced series in mathematical physics•May 1, 1994•0 citations

Excitations with complex wavenumbers in a Hubbard chain I: States with one pair of complex wavenumbers

Ferenc Woynarovich

Advanced series in mathematical physics•May 1, 1994•1 citation

Excitations with complex wavenumbers in a Hubbard chain II: States with several pairse of complex wavenumbers

Ferenc Woynarovich

Advanced series in mathematical physics•May 1, 1994•0 citations

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

Ferenc Woynarovich

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.

Advanced series in mathematical physics•May 1, 1994•1 citation
For pt.I see ibid., vol.15, no.1, p.85 (1982). States of the 1D Hubbard chain with several pairs of complex wavenumbers are studied. The original set of Lieb-Wu equations (1968) is replaced by an equivalent set in which only real wavenumbers appear. These equations are reduced for the states in which the spin degrees of freedom are not excited. The energy-momentum dispersion for these states is also found.
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 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.