Eliashvili, Merab and Japaridze, G.I. and Tsitsishvili, George (2012) Quantum group on a honeycomb lattice. Proceedings of A. Razmadze Mathematical Institute, 160 (3). pp. 3551.

Text
2012_Proc_RMI_160_35.pdf Download (328kB)  Preview 
Abstract
The tightbinding model of electrons on a honeycomb lattice is studied in the presence of a homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux the oneparticle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations on a complex plane. For the special values of quasimomentum the entangled system admits solutions in terms of polynomials. In that case the system exhibits certain symmetry relations allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying the locations of the roots of polynomials on a complex plane and consequently the oneparticle wave functions are found. Employing numeric analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of oneparticle states 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 20:03 
Last Modified:  03 Apr 2015 06:20 
URI:  http://eprints.iliauni.edu.ge/id/eprint/841 
Actions (login required)
View Item 