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

Philosophical Magazine Letters

Excitonic states in the one-dimensional Hubbard model

M. Gulácsi, A. R. Bishop

Published Jan 1, 1998• 0 citations
Publisher

Abstract

We consider the charge excitations of the half-filled Hubbard chain, which are related to electron pairs occupying the same lattice site. In the exact Bethe Ansatzeigen function, we separate the centre-off-mass motion by introducing the centre off-mass and relative coordinates and wave vectors. These excitations are then interpreted as interacting quasi-particles propagating as plane waves along the chain. The two-body problem is solved for these quasi-particles. The solution suggests the existence of bound pairs, namely particle-hole excitonic states. A connection to the magnon states of the ferromagnetic Heisenberg chain is also discussed.

DOI
10.1080/095008398178778

Related papers

Excitons and optical absorption in one-dimensional extended Hubbard models with short- and long-range interactions

Frank B. Gallagher, S. Mazumdar

We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the $1/r$ form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.

Physical review. B, Condensed matter•Dec 15, 1997•68 citations

On the bound state of holes for the square-lattice Hubbard model with resonating valence bonds

А. Ф. Барабанов, Leonid A. Maksimov, Andrey V. Mikheyenkov

The Hubbard model for the square planar lattice in the limit t/U<<1 is discussed. The ground state is chosen to be the product of the Hubbard model's exact solutions for four-site blocks. One-particle excitations appear to be Fermi particles with spin 1 / 2 . Their effective mass near the bottom of the band coincides with the effective mass of excitations in the paramagnetic state in the 'Hubbard-I' approximation. However, minima of the spectrum are situated at other points in the Brillouin zone. The possibility of the binding of two excitations into singlet pair with charge 2e is demonstrated. Cohesive energy is calculated to be equal to 0.1t. The superfluid state of the Bose gas of such pairs is assumed to be connected with high-T c superconductivity.

Journal of Physics Condensed Matter•Dec 18, 1989•10 citations

One- and two-hole excitation spectra of the Hubbard model in the non-half-filled case

Andrzej M. Oleś, Guy Tréglia, D. Spanjaard +1 more

Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.

Physical review. B, Condensed matter•Oct 15, 1986•17 citations

GROUND-STATE PROPERTIES AND ELEMENTARY EXCITATIONS OF THE ONE-DIMENSIONAL HUBBARD MODEL

J. M. P. Carmelo, D. Baeriswyl

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.

International Journal of Modern Physics B•Oct 1, 1988•7 citations

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

Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

Alberto Nocera, N. D. Patel, Jaime A. Fernandez-Baca +2 more

We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing $U/t$ converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of $U/t$ of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

arXiv:1608.07717•Physical review. B./Physical review. B•Nov 28, 2016•18 citations
We consider the charge excitations of the half-filled Hubbard chain, which are related to electron pairs occupying the same lattice site. In the exact Bethe Ansatzeigen function, we separate the centre-off-mass motion by introducing the centre off-mass and relative coordinates and wave vectors. These excitations are then interpreted as interacting quasi-particles propagating as plane waves along the chain. The two-body problem is solved for these quasi-particles. The solution suggests the existence of bound pairs, namely particle-hole excitonic states. A connection to the magnon states of the ferromagnetic Heisenberg chain is also discussed.
We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the 1/r1/r1/r form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.
The Hubbard model for the square planar lattice in the limit t/U<<1 is discussed. The ground state is chosen to be the product of the Hubbard model's exact solutions for four-site blocks. One-particle excitations appear to be Fermi particles with spin 1 / 2 . Their effective mass near the bottom of the band coincides with the effective mass of excitations in the paramagnetic state in the 'Hubbard-I' approximation. However, minima of the spectrum are situated at other points in the Brillouin zone. The possibility of the binding of two excitations into singlet pair with charge 2e is demonstrated. Cohesive energy is calculated to be equal to 0.1t. The superfluid state of the Bose gas of such pairs is assumed to be connected with high-T c superconductivity.
Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.
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.
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.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.