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Quasi‐Spin and the pseudo‐orthogonal group in the hubbard model
Author(s) -
Gould M. D.,
Paldus J.,
čížek J.
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560500306
Subject(s) - hubbard model , hamiltonian (control theory) , irreducible representation , symmetry group , mathematical physics , physics , lattice (music) , spin representation , group (periodic table) , quantum mechanics , combinatorics , mathematics , lie algebra , geometry , superconductivity , fundamental representation , mathematical optimization , acoustics , weight
In this article, we demonstrate a complementarity between the quasi‐spin SU(2) algebra of the Hubbard model and the pseudo‐orthogonal group O( m , m ), where n = 2 m is the number of lattice sites. It is shown that all N ‐electron states for the one‐dimensional Hubbard model, corresponding to given values of spin and quasi‐spin, give rise to an irreducible representation of O( m , m ). Moreover, the cyclic group C n symmetry of the Hamiltonian is investigated and the O( m , m ) ↓ C n branching rules are determined with the use of the U ( n ) q ‐dimension formula. © 1994 John Wiley & Sons, Inc.
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