1,662 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
S-duality in SU(3) Yang-Mills Theory with Non-abelian Unbroken Gauge Group
It is observed that the magnetic charges of classical monopole solutions in
Yang-Mills-Higgs theory with non-abelian unbroken gauge group are in
one-to-one correspondence with coherent states of a dual or magnetic group
. In the spirit of the Goddard-Nuyts-Olive conjecture this
observation is interpreted as evidence for a hidden magnetic symmetry of
Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2)
is studied in detail. The action of the magnetic group on semi-classical states
is given explicitly. Investigations of dyonic excitations show that electric
and magnetic symmetry are never manifest at the same time: Non-abelian magnetic
charge obstructs the realisation of electric symmetry and vice-versa. On the
basis of this fact the charge sectors in the theory are classified and their
fusion rules are discussed. Non-abelian electric-magnetic duality is formulated
as a map between charge sectors. Coherent states obey particularly simple
fusion rules, and in the set of coherent states S-duality can be formulated as
an SL(2,Z)-mapping between sectors which leaves the fusion rules invariant.Comment: 27 pages, harvmac, amssym, one eps figure; minor misprints corrected
and title amende
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
Tensor product representations of the quantum double of a compact group
We consider the quantum double D(G) of a compact group G, following an
earlier paper. We use the explicit comultiplication on D(G) in order to build
tensor products of irreducible *-representations. Then we study their behaviour
under the action of the R-matrix, and their decomposition into irreducible
*-representations. The example of D(SU(2)) is treated in detail, with explicit
formulas for direct integral decomposition (`Clebsch-Gordan series') and
Clebsch-Gordan coefficients. We point out possible physical applications.Comment: LaTeX2e, 27 pages, corrected references, accepted by Comm.Math.Phy
Defect mediated melting and the breaking of quantum double symmetries
In this paper, we apply the method of breaking quantum double symmetries to
some cases of defect mediated melting. The formalism allows for a systematic
classification of possible defect condensates and the subsequent confinement
and/or liberation of other degrees of freedom. We also show that the breaking
of a double symmetry may well involve a (partial) restoration of an original
symmetry. A detailed analysis of a number of simple but representative examples
is given, where we focus on systems with global internal and external (space)
symmetries. We start by rephrasing some of the well known cases involving an
Abelian defect condensate, such as the Kosterlitz-Thouless transition and
one-dimensional melting, in our language. Then we proceed to the non-Abelian
case of a hexagonal crystal, where the hexatic phase is realized if
translational defects condense in a particular rotationally invariant state.
Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference
- …