335 research outputs found
Superconductivity in a system of interacting spinful semions
Non-interacting particles obeying certain fractional statistics have been
predicted to exhibit superconductivity. We discuss the issue in an attractively
interacting system of spinful semions on a lattice by numerically investigating
the presence of off-diagonal long-range order at zero temperature. For this
purpose, we construct a Hubbard model wherein two semions with opposite spin
can virtually coincide while maintaining consistency with the fractional
braiding statistics. Clear off-diagonal long range order is seen in the strong
coupling limit, consistent with the expectation that a pair of semions obeys
Bose statistics. We find that the semion system behaves similarly to a system
of fermions with the same attractive Hubbard interaction for a wide range
of , suggesting that semions also undergo a BCS to BEC crossover as a
function of .Comment: 10 pages, 10 figure
Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect
While a parent Hamiltonian for Laughlin wave function has been long
known in terms of the Haldane pseudopotentials, no parent Hamiltonians are
known for the lowest-Landau-level projected wave functions of the composite
fermion theory at with . If one takes the two lowest Landau
levels to be degenerate, the Trugman-Kivelson interaction produces the
unprojected 2/5 wave function as the unique zero energy solution. If the lowest
three Landau levels are assumed to be degenerate, the Trugman-Kivelson
interaction produces a large number of zero energy states at . We
propose that adding an appropriately constructed three-body interaction yields
the unprojected wave function as the unique zero energy solution, and
report extensive exact diagonalization studies that provide strong support to
this proposal.Comment: 11 pages, 2 figure
Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
Particles obeying non-Abelian braid statistics have been predicted to emerge
in the fractional quantum Hall effect. In particular, a model Hamiltonian with
short-range three-body interaction () between electrons
confined to the lowest Landau level provides exact solutions for quasiholes,
and thereby allows a proof of principle for the existence of quasiholes obeying
non-Abelian braid statistics. We construct, in terms of two- and three- body
Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for
both quasiholes and quasiparticles, and provide evidence of non-Abelian
statistics for the latter as well. The structure of the quasiparticle states of
this model is in agreement with that predicted by the bipartite
composite-fermion model of quasiparticles with exact lowest Landau level
projection. We further demonstrate adiabatic continuity for the ground state,
the ordinary neutral excitation, and the topological exciton as we deform our
model Hamiltonian continuously into the lowest Landau-level
Hamiltonian.Comment: 15 pages, 10 figure
- …