8,942 research outputs found
Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure
Two types of Gaussian processes, namely the Gaussian field with generalized
Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy
covariance (GSGCC) are considered. Some of the basic properties and the
asymptotic properties of the spectral densities of these random fields are
studied. The associated self-similar random fields obtained by applying the
Lamperti transformation to GFGCC and GSGCC are studied.Comment: 32 pages, 6 figure
Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
We demonstrate the semiclassical nature of symmetry twist defects that differ
from quantum deconfined anyons in a true topological phase by examining
non-abelian crystalline defects in an abelian lattice model. An underlying
non-dynamical ungauged S3-symmetry labels the quasi-extensive defects by group
elements and gives rise to order dependent fusion. A central subgroup of local
Wilson observables distinguishes defect-anyon composites by species, which can
mutate through abelian anyon tunneling by tuning local defect phase parameters.
We compute a complete consistent set of primitive basis transformations, or
F-symbols, and study braiding and exchange between commuting defects. This
suggests a modified spin-statistics theorem for defects and non-modular group
structures unitarily represented by the braiding S and exchange T matrices.
Non-abelian braiding operations in a closed system represent the sphere braid
group projectively by a non-trivial central extension that relates the
underlying symmetry.Comment: 44 pages, 43 figure
Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States
We describe the braiding statistics of topological twist defects in abelian
bosonic bilayer (mmn) fractional quantum Hall (FQH) states, which reduce to the
Z_n toric code when m=0. Twist defects carry non-abelian fractional
Majorana-like characteristics. We propose local statistical measurements that
distinguish the fractional charge, or species, of a defect-quasiparticle
composite. Degenerate ground states and basis transformations of a multi-defect
system are characterized by a consistent set of fusion properties. Non-abelian
unitary exchange operations are determined using half braids between defects,
and projectively represent the sphere braid group in a closed system. Defect
spin statistics are modified by equating exchange with 4\pi rotation. The
braiding S matrix is identified with a Dehn twist (instead of a \pi/2 rotation)
on a torus decorated with a non-trivial twofold branch cut, and represents the
congruent subgroup \Gamma_0(2) of modular transformations.Comment: 6 pages, 3 figure
Majorana Fermions and Non-Abelian Statistics in Three Dimensions
We show that three dimensional superconductors, described within a Bogoliubov
de Gennes framework can have zero energy bound states associated with pointlike
topological defects. The Majorana fermions associated with these modes have
non-Abelian exchange statistics, despite the fact that the braid group is
trivial in three dimensions. This can occur because the defects are associated
with an orientation that can undergo topologically nontrivial rotations. A new
feature of three dimensional systems is that there are "braidless" operations
in which it is possible to manipulate the groundstate associated with a set of
defects without moving or measuring them. To illustrate these effects we
analyze specific architectures involving topological insulators and
superconductors.Comment: 4 pages, 2 figures, published versio
From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
Weyl and Dirac (semi)metals in three dimensions have robust gapless
electronic band structures. Their massless single-body energy spectra are
protected by symmetries such as lattice translation, (screw) rotation and time
reversal. In this manuscript, we discuss many-body interactions in these
systems. We focus on strong interactions that preserve symmetries and are
outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a
model based on a three dimensional array of coupled Dirac wires, we show (1)
the Dirac (semi)metal can acquire a many-body excitation energy gap without
breaking the relevant symmetries, and (2) interaction can enable an anomalous
Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the
single-body setting and can only be present holographically on the boundary of
a four dimensional weak topological insulator. Both of these topological states
support fractional gapped (gapless) bulk (resp. boundary) quasiparticle
excitations.Comment: 29 pages, 19 figures. This version has an expanded 'Summary of
Results' and 'Conclusion and Discussion' section to make it more accessible
to a broader audienc
- …