Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2012-03-12
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, 5 figures
Scientific paper
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 unit 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 the 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.
Eliashvili Merab
Japaridze George I.
Tsitsishvili George
No associations
LandOfFree
Quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-489074