Holon and spinon selection rules of the one-dimensional Hubbard model

In the first paper of this series it was found that the $η$ -spin 1/2 holons, spin 1/2 spinons, and $c$ 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 the first paper of this series it was found that the $η$-spin 1/2 holons, spin 1/2 spinons, and $c$ 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.

arXiv:cond-mat/0303279Mar 14, 20030 citations

One-Dimensional Hubbard Models

Florian Gebhard

Springer tracts in modern physicsJan 1, 19971 citation

Spinons and holons for the one-dimensional three-band Hubbard models of high-temperature superconductors.

Jamil Tahir‐Kheli, William A. Goddard

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.

Proceedings of the National Academy of SciencesNov 1, 19932 citations

Spin-charge separation in the 1D Hubbard model

Mona Berciu, Sajeev John

APSMar 1, 20000 citations

Elementary Excitations of One-Dimensional t−J Model with Inverse-Square Exchange

Zou Ha, F. D. M. Haldane

We identify exact excitation content of the intermediate states for the one-particle Green's functions, spin-spin, and (charge) density-density correlation functions of the periodic one-dimensional $t\ensuremath{-}J$ model with inverse-square exchange. The excitations consist of neutral $S=\frac{1}{2}$ spinons and spinless (charge $\ensuremath{-}e$ holons with semionic fractional statistics and bosonic (charge $+2e$ ) "antiholons" which are excitations of the holon condensate. We find a set of selection rules and the regions of nonvanishing spectral weight in the energy-momentum space for the various correlation functions.We identify exact excitation content of the intermediate states for the one-particle Green's functions, spin-spin, and (charge) density-density correlation functions of the periodic one-dimensional $t\ensuremath{-}J$ model with inverse-square exchange. The excitations consist of neutral $S=\frac{1}{2}$ spinons and spinless (charge $\ensuremath{-}e$ holons with semionic fractional statistics and bosonic (charge $+2e$) "antiholons" which are excitations of the holon condensate. We find a set of selection rules and the regions of nonvanishing spectral weight in the energy-momentum space for the various correlation functions.

arXiv:cond-mat/9406059Physical Review LettersNov 21, 199438 citations

In the first paper of this series it was found that the

η

-spin 1/2 holons, spin 1/2 spinons, and

c

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.

S=\frac{1}{2}

spinons and spinless (charge $\ensuremath{-}e$ holons with semionic fractional statistics and bosonic (charge

+2e

) "antiholons" which are excitations of the holon condensate. We find a set of selection rules and the regions of nonvanishing spectral weight in the energy-momentum space for the various correlation functions.