21 citations · 52 across the 13 of their papers we have counts for
13 papers
Group Structure of Wilson Loops in 2D Models with 2- and 4-Band Energy Spectra
T. Supatashvili, M. Eliashvili, G. Tsitsishvili
We consider a tight-binding model defined by a matrix Hamiltonian over 2D Brillouin zone. Multiband energy spectrum gives rise to a non-Abelian gauge structure set by the Berry con…
Edge States of a Periodic Chain with Four-Band Energy Spectrum
M. Eliashvili, D. Kereselidze, G. Tsitsishvili +1
Tight-binding model on a finite chain is studied with four-fold alternated hopping parameters . Imposing the open boundary conditions, the corresponding recursion is s…
Boundary Conditions and Formation of Pure Spin Currents in Magnetic Field
Merab Eliashvili, George Tsitsishvili
Schrödinger equation for an electron confined to a two-dimensional strip is considered in the presence of homogeneous orthogonal magnetic field. Since the system has edges, the eig…
Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials
M. Eliashvili, G. I. Japaridze, G. Tsitsishvili +1
Analytic technique based on Chebyshev polynomials is developed for studying two-dimensional lattice ribbons with hopping anisotropy. In particular, the tight-binding models on squa…
The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice
Merab Eliashvili, George I. Japaridze, George Tsitsishvili
The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is ra…
On the NCCS model of the quantum Hall fluid
M. Eliashvili, G. Tsitsishvili
Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the integer quantum Hall effect (IQHE) state on the fractional quantum Hal…
Ground-State Structure in Bilayer Quantum Hall Systems
Z. F. Ezawa, M. Eliashvili, G. Tsitsishvili
We investigate the ground-state structure of the bilayer quantum Hall system at the filling factor . Making an exact analysis of the ground state in the SU(4)-invariant limit,…
Area Preserving Transformations in Non-commutative Space and NCCS Theory
M. Eliashvili, G. Tsitsishvili
We propose an heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformation of the classical…
Geometric Transformations and NCCS Theory in the Lowest Landau Level
M. Eliashvili, G. Tsitsishvili
Chern-Simons type gauge field is generated by the means of the singular area preserving transformations in the lowest Landau level of electrons forming fractional quantum Hall stat…
Exact Symmetries of Electron Interactions in the Lowest Landau Level
M. Eliashvili, Z. F. Ezawa, G. Tsitsishvili
Considering the system of interacting electrons in the lowest Landau level we show that the corresponding four-fermion Hamiltonian is invariant with respect to the local area-prese…
Magnetic Instability in a Parity Invariant 2D Fermion System
M. Eliashvili, G. Tsitsishvili
We consider the parity invariant (2+1)-dimensional QED where the matter is represented as a mixture of fermions with opposite spins. It is argued that the perturbative ground state…
Chern-Simons Theory and Quantum Fields in the Lowest Landau Level
M. Eliashvili, G. Tsitsishvili
By considering the area preserving geometric transformations in the configuration space of electrons moving in the lowest Landau level (LLL) we arrive at the Chern-Simons type Lagr…
Magnetic moment interaction in the anyon superconductor
M. Eliashvili, G. Tsitsishvili
Magnetic moment interaction is shown to play a defining role in the magnetic properties of anyon superconductors. The necessary condition for the existence of the Meissner effect i…