Steve Simon

Abstract:

We demonstrate numerically that non-Abelian quasihole (qh) excitations of the ν=5/2 fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the qh spacing is increased, the unitary transformation which describes winding two qh's around each other converges exponentially to its asymptotic limit and that the two orthogonal wave functions describing a system with four qh's become exponentially degenerate. We calculate the length scales for these two decays to be ξU2.70 and ξE2.30, respectively. Additionally, we determine which fusion channel is lower in energy when two qh's are brought close together. © 2009 The American Physical Society.

Abstract:

We propose an experiment to explore the magnetic phase transitions in interacting fermionic Hubbard systems and describe how to obtain the ferromagnetic phase diagram of itinerant-electron systems from these observations. In addition, signatures of ferromagnetic correlations in the observed ground states are found: for large trap radii (trap radius RT >4, in units of coherence length ξ), ground states are topological in nature-a "skyrmion" in two dimension, and a "hedgehog" in three dimension. © 2009 The American Physical Society.