772 research outputs found
SPINON BASIS FOR (sl2^)_k INTEGRABLE HIGHEST WEIGHT MODULES AND NEW CHARACTER FORMULAS
In this note we review the spinon basis for the integrable highest weight
modules of sl2^ at levels k\geq1, and give the corresponding character formula.
We show that our spinon basis is intimately related to the basis proposed by
Foda et al. in the principal gradation of the algebra. This gives rise to new
identities for the q-dimensions of the integrable modules.Comment: 9 pages, plain TeX + amssym.def, to appear in the proceedings of
`Statistical Mechanics and Quantum Field Theory,' USC, May 16-21, 199
Perturbed vortex lattices and the stability of nucleated topological phases
We study the stability of nucleated topological phases that can emerge when
interacting non-Abelian anyons form a regular array. The studies are carried
out in the context of Kitaev's honeycomb model, where we consider three
distinct types of perturbations in the presence of a lattice of Majorana mode
binding vortices -- spatial anisotropy of the vortices, dimerization of the
vortex lattice and local random disorder. While all the nucleated phases are
stable with respect to weak perturbations of each kind, strong perturbations
are found to result in very different behavior. Anisotropy of the vortices
stabilizes the strong-pairing like phases, while dimerization can recover the
underlying non-Abelian phase. Local random disorder, on the other hand, can
drive all the nucleated phases into a gapless thermal metal state. We show that
all these distinct behavior can be captured by an effective staggered
tight-binding model for the Majorana modes. By studying the pairwise
interactions between the vortices, i.e. the amplitudes for the Majorana modes
to tunnel between vortex cores, the locations of phase transitions and the
nature of the resulting states can be predicted. We also find that due to
oscillations in the Majorana tunneling amplitude, lattices of Majorana modes
may exhibit a Peierls-like instability, where a dimerized configuration is
favored over a uniform lattice. As the nature of the nucleated phases depends
only on the Majorana tunneling, our results apply also to other system
supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave
superconductors, Wigner crystals in Moore-Read fractional quantum Hall states
or arrays of topological nanowires.Comment: 13 pages, 4 pages of appendices, 24 figures. Published versio
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