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On quantum groups in the Hubbard model with phonons. (English) Zbl 0916.17030

Summary: The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti [Phys. Rev. Lett. 72, 1730 ff (1994)] is derived for a \(D\)-dimensional lattice. It is shown that the superconducting \(SU_q(2)\) holds as a true quantum symmetry only for \(D=1\) and that terms of higher order in the fermionic operators are needed in addition to phonons. A discussion of quantum symmetries in general is given in a formalism that should be readily accessible to non-Hopf algebraists.

MSC:

17B81 Applications of Lie (super)algebras to physics, etc.
81V70 Many-body theory; quantum Hall effect
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T25 Quantum field theory on lattices
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