Quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice

Eliashvili, Merab and Japaridze, G.I. and Tsitsishvili, George (2012) Quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice. Journal of Physics A: Mathematical and General, 45 (9). pp. 395305-1.


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The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of a homogeneous magnetic field. Provided the magnetic flux per uni t hexagon is rational of the elementary flux, the one-particle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of the quantum group $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations on a complex plane. For the special values of quasi-momentum the entangled system admits solutions in terms of polynomials. In that case the system exhibits certain symmetry allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying locations of the roots of polynomials on the complex plane are found. Employing numerical analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrammes exhibiting the ordered structure of one-particle eigenstates are depicted.

Item Type: Article
Subjects: Q Science > QC Physics
Divisions: Faculties/Schools > School of Natural Sciences and Engineering
Depositing User: გიორგი ჯაფარიძე
Date Deposited: 30 Jan 2014 20:02
Last Modified: 03 Apr 2015 06:20
URI: http://eprints.iliauni.edu.ge/id/eprint/715

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