Quantum and classical localization in the lowest Landau level

Anyons and Lowest Landau Level Anyons

Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the anyonic nature of particle...

The Electromagnetic Interactions of Electrons in the Lowest Landau Level

Starting from a system of planar electrons in a strong magnetic field normal to the plane, interacting with perturbing electromagnetic fields, an effective Lagrangian for the fermions in the lowest Landau level (L.L.L.) has been derived. By choosing a suitable background electrostatic potential, an incompressible droplet of these electrons is constructed. The gauge invariant effective Lagrangia...

Interacting electrons in graphene nanoribbons in the lowest Landau level

Exact Diagonalization Of The Fractional Quantum Hall Many-Body Hamiltonian In The Lowest Landau Level

For a gaussian interaction V (x, y) = λ e− x2+y2 2r2 with long range r >> lB, lB the magnetic length, we rigorously prove that the eigenvalues of the finite volume Hamiltonian HN,LL = PLLHNPLL, HN = ∑N i=1 ( −i~∇xi − eA(xi) 2 + ∑ i,j; i6=j V (xi − xj), rotA = (0, 0, B), and PLL the projection onto the lowest Landau level, are given by the following set: Let M be the number of flux quanta flowin...

Possible reentrance of the fractional quantum Hall effect in the lowest Landau level.

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = ...