744 research outputs found
Endstates in multichannel spinless p-wave superconducting wires
Multimode spinless p-wave superconducting wires with a width W much smaller
than the superconducting coherence length \xi are known to have multiple
low-energy subgap states localized near the wire's ends. Here we compare the
typical energies of such endstates for various terminations of the wire: A
superconducting wire coupled to a normal-metal stub, a weakly disordered
superconductor wire and a wire with smooth confinement. Depending on the
termination, we find that the energies of the subgap states can be higher or
lower than for the case of a rectangular wire with hard-wall boundaries.Comment: 10 pages, 7 figure
Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model
The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost
Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model
We develop a rigorous and highly accurate technique for calculation of the
Berry phase in systems with a quadratic Hamiltonian within the context of the
Kitaev honeycomb lattice model. The method is based on the recently found
solution of the model which uses the Jordan-Wigner-type fermionization in an
exact effective spin-hardcore boson representation. We specifically simulate
the braiding of two non-Abelian vortices (anyons) in a four vortex system
characterized by a two-fold degenerate ground state. The result of the braiding
is the non-Abelian Berry matrix which is in excellent agreement with the
predictions of the effective field theory. The most precise results of our
simulation are characterized by an error on the order of or lower. We
observe exponential decay of the error with the distance between vortices,
studied in the range from one to nine plaquettes. We also study its correlation
with the involved energy gaps and provide preliminary analysis of the relevant
adiabaticity conditions. The work allows to investigate the Berry phase in
other lattice models including the Yao-Kivelson model and particularly the
square-octagon model. It also opens the possibility of studying the Berry phase
under non-adiabatic and other effects which may constitute important sources of
errors in topological quantum computation.Comment: 27 pages, 9 figures, 3 appendice
Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
We theoretically study an exactly solvable Gamma matrix generalization of the
Kitaev spin model on the ruby lattice, which is a honeycomb lattice with
"expanded" vertices and links. We find this model displays an exceptionally
rich phase diagram that includes: (i) gapless phases with stable spin fermi
surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band
touching points, and (iii) gapped phases with finite Chern numbers possessing
the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to
include Ising-like interactions that break the exact solvability of the model
in a controlled manner. When these terms are dominant, they lead to a trivial
Ising ordered phase which is shown to be adiabatically connected to a large
coupling limit of the exactly solvable phase. In the limit when these
interactions are weak, we treat them within mean-field theory and present the
resulting phase diagrams. We discuss the nature of the transitions between
various phases. Our results highlight the richness of possible ground states in
closely related magnetic systems.Comment: 9 pages, 9 figure
A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
We present a solution of Kitaev's spin model on the honeycomb lattice and of
related topologically ordered spin models. We employ a Jordan-Wigner type
fermionization and find that the Hamiltonian takes a BCS type form, allowing
the system to be solved by Bogoliubov transformation. Our fermionization does
not employ non-physical auxiliary degrees of freedom and the eigenstates we
obtain are completely explicit in terms of the spin variables. The ground-state
is obtained as a BCS condensate of fermion pairs over a vacuum state which
corresponds to the toric code state with the same vorticity. We show in detail
how to calculate all eigenstates and eigenvalues of the model on the torus. In
particular, we find that the topological degeneracy on the torus descends
directly from that of the toric code, which now supplies four vacua for the
fermions, one for each choice of periodic vs. anti-periodic boundary
conditions. The reduction of the degeneracy in the non-Abelian phase of the
model is seen to be due to the vanishing of one of the corresponding candidate
BCS ground-states in that phase. This occurs in particular in the fully
periodic vortex-free sector. The true ground-state in this sector is exhibited
and shown to be gapped away from the three partially anti-periodic
ground-states whenever the non-Abelian phase is gapped.Comment: 10 pages, 4 figure
Multi-wavelength Observations of Dusty Star Formation at Low and High Redshift
This paper examines what can be learned about high-redshift star formation
from the small fraction of high-redshift galaxies' luminosities that is emitted
at accessible wavelengths. We review and quantify empirical correlations
between bolometric luminosities produced by star formation and the UV, mid-IR,
sub-mm, and radio luminosities of galaxies in the local universe. These
correlations suggest that observations of high-redshift galaxies at any of
these wavelengths should constrain their star-formation rates to within
0.2--0.3 dex. We assemble the limited evidence that high-redshift galaxies obey
these locally calibrated correlations. The characteristic luminosities and dust
obscurations of galaxies at z ~ 0, z ~ 1, and z ~ 3 are reviewed. After
discussing the relationship between the high-redshift populations selected in
surveys at different wavelengths, we calculate the contribution to the 850um
background from each. The available data show that a correlation between
star-formation rate and dust obscuration L_dust/L_UV exists at low and high
redshift. This correlation plays a central role in the major conclusion of this
paper: most star formation at high redshift occurred in galaxies with 1 <
L_dust/L_UV < 100 similar to those that host the majority of star formation in
the local universe and to those that are detected in UV-selected surveys.
(abridged)Comment: Scheduled for publication in ApJ v544 Dec 2000. Significant changes
to section 4. Characteristic UV and dust luminosities of star-forming
galaxies at redshifts z~0, z~1, and z~3 presented. Existence of extremely
obscured galaxies more clearly acknowledged. Original conclusions reinforced
by the observed correlation between bolometric luminosity and dust
obscuration at 0<z<
Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
We study the collective states of interacting non-Abelian anyons that emerge
in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to
lead to the lifting of the topological degeneracy and the energy is discovered
to exhibit oscillations that are consistent with Majorana fermions being
localized at vortex cores. We show how to construct states corresponding to the
fusion channel degrees of freedom and obtain the energy gaps characterizing the
stability of the topological low energy spectrum. To study the collective
behavior of many vortices, we introduce an effective lattice model of Majorana
fermions. We find necessary conditions for it to approximate the spectrum of
the honeycomb lattice model and show that bi-partite interactions are
responsible for the degeneracy lifting also in many vortex systems.Comment: 22 pages, 12 figures, published versio
Kaleidoscope of topological phases with multiple Majorana species
Exactly solvable lattice models for spins and non-interacting fermions
provide fascinating examples of topological phases, some of them exhibiting the
localized Majorana fermions that feature in proposals for topological quantum
computing. The Chern invariant is one important characterization of such
phases. Here we look at the square-octagon variant of Kitaev's honeycomb model.
It maps to spinful paired fermions and enjoys a rich phase diagram featuring
distinct abelian and nonabelian phases with and . The and phases all support localized Majorana
modes and are examples of Ising and anyon theories respectively.Comment: 6 pages, 5 figures. The second version has a new title, reflecting a
change of focus of the presentation in this version. The third version
contains minor changes and is essentially the one published in New Journal of
Physic
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
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