2 research outputs found
Non-Abelian Braiding of Lattice Bosons
We report on a numerical experiment in which we use time-dependent potentials
to braid non-abelian quasiparticles. We consider lattice bosons in a uniform
magnetic field within the fractional quantum Hall regime, where , the
ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce
time-dependent potentials which move quasiparticle excitations around one
another, explicitly simulating a braiding operation which could implement part
of a gate in a quantum computation. We find that different braids do not
commute for near and , with Berry matrices respectively
consistent with Ising and Fibonacci anyons. Near , the braids commute.Comment: 5 pages, 1 figur
Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
We study lattice models of charged particles in uniform magnetic fields. We
show how longer range hopping can be engineered to produce a massively
degenerate manifold of single-particle ground states with wavefunctions
identical to those making up the lowest Landau level of continuum electrons in
a magnetic field. We find that in the presence of local interactions, and at
the appropriate filling factors, Laughlin's fractional quantum Hall
wavefunction is an exact many-body ground state of our lattice model. The
hopping matrix elements in our model fall off as a Gaussian, and when the flux
per plaquette is small compared to the fundamental flux quantum one only needs
to include nearest and next nearest neighbor hoppings. We suggest how to
realize this model using atoms in optical lattices, and describe observable
consequences of the resulting fractional quantum Hall physics.Comment: 4 pages, 3 figures. Published versio