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A new topological aspect of the arbitrary dimensional topological defects
We present a new generalized topological current in terms of the order
parameter field to describe the arbitrary dimensional topological
defects. By virtue of the -mapping method, we show that the topological
defects are generated from the zero points of the order parameter field , and the topological charges of these topological defects are topological
quantized in terms of the Hopf indices and Brouwer degrees of -mapping
under the condition that the Jacobian . When , it is shown that there exist the crucial case of branch process.
Based on the implicit function theorem and the Taylor expansion, we detail the
bifurcation of generalized topological current and find different directions of
the bifurcation. The arbitrary dimensional topological defects are found
splitting or merging at the degenerate point of field function but
the total charge of the topological defects is still unchanged.Comment: 24 pages, 10 figures, Revte
Topological defects of N\'eel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
Heavy fermion systems represent a prototypical setting to study magnetic
quantum phase transitions. A particular focus has been on the physics of Kondo
destruction, which captures quantum criticality beyond the Landau framework of
order-parameter fluctuations. In this context, we study the spin one-half
Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is
approached from the Kondo destroyed, antiferromagnetically ordered insulating
phase. We describe the local moments in terms of a coarse grained quantum
non-linear sigma model, and show that the skyrmion defects of the
antiferromagnetic order parameter host a number of competing order parameters.
In addition to the spin Peierls, charge and current density wave order
parameters, we identify for the first time Kondo singlets as the competing
orders of the antiferromagnetism. We show that the antiferromagnetism and
various competing singlet orders can be related to each other via generalized
chiral transformations of the underlying fermions. We also show that the
conduction electrons acquire a Berry phase through their coupling to the
hedgehog configurations of the N\'eel order, which cancels the Berry phase of
the local moments. Our results demonstrate the competition between the
Kondo-singlet formation and spin-Peierls order when the antiferromagnetic order
is suppressed, thereby shedding new light on the global phase diagram of heavy
fermion systems at zero temperature.Comment: 14 pages, 4 figure
Cross-talk between topological defects in different fields revealed by nematic microfluidics
Topological defects are singularities in material fields that play a vital
role across a range of systems: from cosmic microwave background polarization
to superconductors, and biological materials. Although topological defects and
their mutual interactions have been extensively studied, little is known about
the interplay between defects in different fields -- especially when they
co-evolve -- within the same physical system. Here, using nematic
microfluidics, we study the cross-talk of topological defects in two different
material fields -- the velocity field and the molecular orientational field.
Specifically, we generate hydrodynamic stagnation points of different
topological charges at the center of star-shaped microfluidic junctions, which
then interact with emergent topological defects in the orientational field of
the nematic director. We combine experiments, and analytical and numerical
calculations to demonstrate that a hydrodynamic singularity of given
topological charge can nucleate a nematic defect of equal topological charge,
and corroborate this by creating , and topological defects in
, , and arm junctions. Our work is an attempt toward understanding
materials that are governed by distinctly multi-field topology, where disparate
topology-carrying fields are coupled, and concertedly determine the material
properties and response.Comment: 18 pages, 9 figure
Semilocal Topological Defects
Semilocal defects are those formed in field theories with spontaneously
broken symmetries, where the vacuum manifold is fibred by the action of the
gauge group in a non-trivial way. Studied in this paper is the simplest such
class of theories, in which , fibred by the action of a local
symmetry. Despite having trivial homotopy groups up to ,
this theory exhibits a fascinating variety of defects: vortices, or semilocal
strings; monopoles (on which the strings terminate); and (when ) textures,
which may be stabilised by their associated magnetic field to produce a
skyrmion.Comment: 28pp, DAMTP-HEP-92-2
Scalar fields: from domain walls to nanotubes and fulerenes
In this work we review some features of topological defects in field theory
models for real scalar fields. We investigate topological defects in models
involving one and two or more real scalar fields. In models involving a single
field we examine two different subclasses of models, which support one or more
topological defects. In models involving two or more real scalar fields, we
explore the presence of defects that live inside topological defects, and
junctions and networks of defects. In the case of junctions of defects we
investigte structures that simulate nanotubes and fulerenes. Our investigations
may also be used to describe nonlinear properties of polymers, Langmuir films
and optical solitons in fibers.Comment: Revtex, 10 pages, 5 figures. Talk presented at XXII Encontro Nacional
de Fisica de Particulas e Campos, Sao Lourenco, MG, Brazil, October 2001; v2,
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