91,475 research outputs found
Superconducting Phase with Fractional Vortices in the Frustrated Kagome Wire Network at f=1/2
In classical XY kagome antiferromagnets, there can be a novel low temperature
phase where has quasi-long-range order but is
disordered, as well as more conventional antiferromagnetic phases where
is ordered in various possible patterns ( is the angle of orientation
of the spin). To investigate when these phases exist in a physical system, we
study superconducting kagome wire networks in a transverse magnetic field when
the magnetic flux through an elementary triangle is a half of a flux quantum.
Within Ginzburg-Landau theory, we calculate the helicity moduli of each phase
to estimate the Kosterlitz-Thouless (KT) transition temperatures. Then at the
KT temperatures, we estimate the barriers to move vortices and effects that
lift the large degeneracy in the possible patterns. The effects we have
considered are inductive couplings, non-zero wire width, and the
order-by-disorder effect due to thermal fluctuations. The first two effects
prefer patterns while the last one selects a
pattern of supercurrents. Using the parameters of recent experiments, we
conclude that at the KT temperature, the non-zero wire width effect dominates,
which stabilizes a conventional superconducting phase with a current
pattern. However, by adjusting the experimental parameters, for example by
bending the wires a little, it appears that the novel superconducting
phase can instead be stabilized. The barriers to vortex motion are low enough
that the system can equilibrate into this phase.Comment: 30 pages including figure
Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
Topological color codes are among the stabilizer codes with remarkable
properties from quantum information perspective. In this paper we construct a
four-valent lattice, the so called ruby lattice, governed by a 2-body
Hamiltonian. In a particular regime of coupling constants, degenerate
perturbation theory implies that the low energy spectrum of the model can be
described by a many-body effective Hamiltonian, which encodes the color code as
its ground state subspace. The gauge symmetry
of color code could already be realized by
identifying three distinct plaquette operators on the lattice. Plaquettes are
extended to closed strings or string-net structures. Non-contractible closed
strings winding the space commute with Hamiltonian but not always with each
other giving rise to exact topological degeneracy of the model. Connection to
2-colexes can be established at the non-perturbative level. The particular
structure of the 2-body Hamiltonian provides a fruitful interpretation in terms
of mapping to bosons coupled to effective spins. We show that high energy
excitations of the model have fermionic statistics. They form three families of
high energy excitations each of one color. Furthermore, we show that they
belong to a particular family of topological charges. Also, we use
Jordan-Wigner transformation in order to test the integrability of the model
via introducing of Majorana fermions. The four-valent structure of the lattice
prevents to reduce the fermionized Hamiltonian into a quadratic form due to
interacting gauge fields. We also propose another construction for 2-body
Hamiltonian based on the connection between color codes and cluster states. We
discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version
Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
We analyze the Kitaev model on the triangle-honeycomb lattice whose ground
state has recently been shown to be a chiral spin liquid. We consider two
perturbative expansions: the isolated-dimer limit containing Abelian anyons and
the isolated-triangle limit. In the former case, we derive the low-energy
effective theory and discuss the role played by multi-plaquette interactions.
In this phase, we also compute the spin-spin correlation functions for any
vortex configuration. In the isolated-triangle limit, we show that the
effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at
the isotropic point. We also compute the next-order correction which opens a
gap and yields non-Abelian anyons.Comment: 7 pages, 4 figures, published versio
Spherical Orbifolds for Cosmic Topology
Harmonic analysis is a tool to infer cosmic topology from the measured
astrophysical cosmic microwave background CMB radiation. For overall positive
curvature, Platonic spherical manifolds are candidates for this analysis. We
combine the specific point symmetry of the Platonic manifolds with their deck
transformations. This analysis in topology leads from manifolds to orbifolds.
We discuss the deck transformations of the orbifolds and give eigenmodes for
the harmonic analysis as linear combinations of Wigner polynomials on the
3-sphere. These provide new tools for detecting cosmic topology from the CMB
radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1011.427
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