On the SU(2)×SU(2) symmetry in the Hubbard model

• Authors: Dorota Jakubczyk , Paweł Jakubczyk
• Languages of publication: EN

Abstracts

EN

We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

Keywords

EN

Hubbard model; unitary group; Fourier transform; spin chain

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 4
• Pages: 906-912

Dates

published

1 - 8 - 2012

online

17 - 7 - 2012

Contributors

author

Dorota Jakubczyk

• Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland

author

Paweł Jakubczyk

• Institute of Physics, University of Rzeszów, ul. Rejtana 16C, 35-910, Rzeszów, Poland

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Identifiers

DOI

10.2478/s11534-012-0055-6