Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an int...

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...

Landau Level Mixing and Solenoidal Terms in Lowest Landau Level Currents

We calculate the lowest Landau level (LLL) current by working in the full Hilbert space of a two dimensional electron system in a magnetic field and keeping all the non-vanishing terms in the high field limit. The answer a) is not represented by a simple LLL operator and b) differs from the current operator, recently derived by Martinez and Stone in a field theoretic LLL formalism, by solenoida...

Interacting electrons in graphene nanoribbons in the lowest Landau level

Skyrmion physics beyond the lowest Landau-level approximation

The effects of Landau-level mixing and finite thickness of the two-dimensional electron gas on the relative stability of Skyrmion and single spin-flip excitations at Landau-level filling factor n51 have been investigated. Landau-level mixing is studied by fixed-phase diffusion Monte Carlo, and finite thickness is included by modifying the effective Coulomb interaction. Both Landau-level mixing ...