The Quantum Group and Harper Equation on a Honeycomb Lattice

The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group U q ( sl 2 ). The corresponding Harper equation is rewritten as a system of two...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016-07, Vol.216 (4), p.522-526
Main Authors: Eliashvili, M., Tsitsishvili, G., Japaridze, G.
Format: Article
Language:English
Subjects:
Magnetic fields
Mathematics
Mathematics and Statistics
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Summary:The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group U q ( sl 2 ). The corresponding Harper equation is rewritten as a system of two coupled functional equations in the complex plane. The system is shown to exhibit certain symmetry that allows one to resolve the entanglement, and the basic single equation determining the eigenvalues and eigenstates is obtained. Equations specifying the roots of eigenstates in the complex plane are found.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-2909-8