Related papers: Topological defect system in O(n) symmetric time-d…
We present a new generalized topological current in terms of the order parameter field $\vec \phi$ to describe the arbitrary dimensional topological defects. By virtue of the $% \phi$-mapping method, we show that the topological defects are…
In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian $J(\phi/v) \neq…
In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that the Jacobian $J(\phi/v) \neq 0$. When…
From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution…
In the light of $\phi $--mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are investigated. It is pointed out that the topological quantum…
In the light of $\phi $--mapping method and topological current theory, the topological structure of the vortex state in TDGL model and the topological quantization of the vortex topological charges are investigated. It is pointed out that…
We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the $\phi$-mapping topological current theory. The main purpose in this paper is to present a new theoretical framework which can directly give the…
A novel U(1) topological gauge field theory for topological defects in liquid crystals is constructed by considering the U(1) gauge field is invariant under the director inversion. Via the U(1) gauge potential decomposition theory and the…
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories.…
The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices…
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…
We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the…
O(N) symmetric $\lambda \phi^4$ field theories describe many critical phenomena in the laboratory and in the early Universe. Given N and $D\leq 3$, the dimension of space, these models exhibit topological defect classical solutions that in…
We review the results of arXiv:1208.1481 on orientation reversal and duality for defects in topological Landau-Ginzburg models, with the intention of providing an easily accessible toolkit for computations. As an example we include a proof…
We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
We introduce the notion of $n$-dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special cases of…
We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects…
We present an extension of Landau's theory of phase transitions by incorporating the topology of the order parameter. When the order parameter comprises several components arising from multiplicity in the same irreducible representation of…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…