764 research outputs found
On a core instability of 't Hooft Polyakov monopoles
We discuss a core instability of 't Hooft Polyakov monopoles in Alice
electrodynamics type of models in which charge conjugation symmetry is gauged.
The monopole may deform into a toroidal defect which carries an Alice flux and
a (non-localizable) magnetic Cheshire charge.Comment: 7 pages, 4 figure
Topological entanglement entropy relations for multi phase systems with interfaces
We study the change in topological entanglement entropy that occurs when a
two-dimensional system in a topologically ordered phase undergoes a transition
to another such phase due to the formation of a Bose condensate. We also
consider the topological entanglement entropy of systems with domains in
different topological phases, and of phase boundaries between these domains. We
calculate the topological entropy of these interfaces and derive two
fundamental relations between the interface topological entropy and the bulk
topological entropies on both sides of the interface.Comment: 4 pages, 3 figures, 2 tables, revte
Condensate induced transitions between topologically ordered phases
We investigate transitions between topologically ordered phases in two
spatial dimensions induced by the condensation of a bosonic quasiparticle. To
this end, we formulate an extension of the theory of symmetry breaking phase
transitions which applies to phases with topological excitations described by
quantum groups or modular tensor categories. This enables us to deal with
phases whose quasiparticles have non-integer quantum dimensions and obey braid
statistics. Many examples of such phases can be constructed from
two-dimensional rational conformal field theories and we find that there is a
beautiful connection between quantum group symmetry breaking and certain
well-known constructions in conformal field theory, notably the coset
construction, the construction of orbifold models and more general conformal
extensions. Besides the general framework, many representative examples are
worked out in detail.Comment: 27 pages, 3 figures, RevTe
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
Noncompact dynamical symmetry of a spin-orbit coupled oscillator
We explain the finite as well as infinite degeneracy in the spectrum of a
particular system of spin-1/2 fermions with spin-orbit coupling in three
spatial dimensions. Starting from a generalized Runge-Lenz vector, we
explicitly construct a complete set of symmetry operators, which span a
noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only
involves a particular, infinite, so called singleton representation. In the
branch where orbital and spin angular momentum are aligned the full
representation appears, constituting a 3D analogue of Landau levels.
Anti-aligning the spin leads to a finite degeneracy due to a truncation of the
singleton representation. We conclude the paper by constructing the spectrum
generating algebra of the problem
Diagrammatics for Bose condensation in anyon theories
Phase transitions in anyon models in (2+1)-dimensions can be driven by
condensation of bosonic particle sectors. We study such condensates in a
diagrammatic language and explicitly establish the relation between the states
in the fusion spaces of the theory with the condensate, to the states in the
parent theory using a new set of mathematical quantities called vertex lifting
coefficients (VLCs). These allow one to calculate the full set of topological
data (-, -, - and -matrices) in the condensed phase. We provide
closed form expressions of the topological data in terms of the VLCs and
provide a method by which one can calculate the VLCs for a wide class of
bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary
diagrams directly from the condensed phase to the original phase, such that
they can be evaluated using the data of the original theory and a limited
number of VLCs. Some representative examples are worked out in detail.Comment: 20 pages, 1 figure, many diagram
Simple models with ALICE fluxes
We introduce two simple models which feature an Alice electrodynamics phase. In a well defined sense the Alice flux solutions we obtain in these models obey first order equations similar to those of the Nielsen-Olesen fluxtube in the abelian higgs model in the Bogomol'nyi limit. Some numerical solutions are presented as well
Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole
The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-NUT space with
the time trivially added, is the appropriate background of the Dirac magnetic
monopole without an explicit mass term. One remarks that there exists a very
simple five-dimensional metric of spacetimes carrying massive magnetic
monopoles that is an exact solution of the vacuum Einstein equations. Moreover,
the same isometry properties as the original Euclidean Taub-NUT space are
preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as
a combinations between the Gross-Perry-Sorkin and Schwarzschild ones. The
asymptotic motion of the scalar charged test particles is discussed, now by
accounting for the mixing between the gravitational and magnetic effects.Comment: 7 page
Inequivalent classes of interference experiments with non-abelian anyons
We present a theoretical analysis of inequivalent classes of interference experiments with non-abelian anyons using an idealized Mach-Zender type interferometer. Because of the non-abelian nature of the braid group action one has to distinguish the different possibilities in which the experiment can be repeated, which lead to different interference patterns. We show that each setup will, after repeated measurement, lead to a situation where the two-particle (or multi-particle) state gets locked into an eigenstate of some well defined operator. Also the probability to end up in such an eigenstate is calculated. Some representative examples are worked out in detail
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