2,430 research outputs found
Moran Sets and Hyperbolic Boundaries
In the paper, we prove that a Moran set is homeomorphic to the hyperbolic
boundary of the representing symbolic space in the sense of Gromov, which
generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009),
1777-1795]. Moreover, by making use of this, we establish the Lipschitz
equivalence of a class of Moran sets.Comment: 14 pages, 1 figur
Commuting-projector Hamiltonians for chiral topological phases built from parafermions
We introduce a family of commuting-projector Hamiltonians whose degrees of
freedom involve parafermion zero modes residing in a parent
fractional-quantum-Hall fluid. The two simplest models in this family emerge
from dressing Ising-paramagnet and toric-code spin models with parafermions; we
study their edge properties, anyonic excitations, and ground-state degeneracy.
We show that the first model realizes a symmetry-enriched topological phase
(SET) for which spin-flip symmetry from the Ising paramagnet
permutes the anyons. Interestingly, the interface between this SET and the
parent quantum-Hall phase realizes symmetry-enforced parafermion
criticality with no fine-tuning required. The second model exhibits a
non-Abelian phase that is consistent with topological order,
and can be accessed by gauging the symmetry in the SET.
Employing Levin-Wen string-net models with -graded structure,
we generalize this picture to construct a large class of commuting-projector
models for SETs and non-Abelian topological orders exhibiting
the same relation. Our construction provides the first
commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian
topological order.Comment: 29+18 pages, 25 figure
Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
In the paper, we focus on the connectedness of planar self-affine sets
generated by an integer expanding matrix with and a collinear digit set , where and
such that is linearly independent. We discuss
the domain of the digit to determine the connectedness of
. Especially, a complete characterization is obtained when
we restrict to be an integer. Some results on the general case of are obtained as well.Comment: 15 pages, 10 figure
Giant topological insulator gap in graphene with 5d adatoms
Two-dimensional topological insulators (2D TIs) have been proposed as
platforms for many intriguing applications, ranging from spintronics to
topological quantum information processing. Realizing this potential will
likely be facilitated by the discovery of new, easily manufactured materials in
this class. With this goal in mind we introduce a new framework for engineering
a 2D TI by hybridizing graphene with impurity bands arising from heavy adatoms
possessing partially filled d-shells, in particular osmium and iridium. First
principles calculations predict that the gaps generated by this means exceed
0.2 eV over a broad range of adatom coverage; moreover, tuning of the Fermi
level is not required to enter the TI state. The mechanism at work is expected
to be rather general and may open the door to designing new TI phases in many
materials.Comment: 7 pages, 8 figure
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