93 research outputs found
Magnetic Instability in a Parity Invariant 2D Fermion System
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 of the system is unstable with respect to the
formation of magnetized ground state. Carrying out the finite temperature
analysis we show that the magnetic instability disappears in the high
temperature regime.Comment: 7 pages, RevTe
The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice
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 rational of the elementary flux, the
one-particle Hamiltonian is expressed in terms of the generators of the quantum
group . Employing the functional representation of the quantum group
the Harper equation is rewritten as a systems of two coupled
functional equations in the complex plane. For the special values of
quasi-momentum the entangled system admits solutions in terms of polynomials.
The system is shown to exhibit 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 in the complex plane are found. Employing numerical
analysis the roots of polynomials corresponding to different eigenstates are
solved out and the diagrams exhibiting the ordered structure of one-particle
eigenstates are depicted.Comment: 11 pages, 4 figure
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