Related papers: On measuring the topological charge of anyons
The distinct methods for measuring topological charge in a non-abelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total…
We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that…
The topological nature of Chern-Simons term describing the interaction of a charge with magnetic monopole is manifested in two ways: it changes the plane dynamical geometry of a free particle for the cone dynamical geometry without…
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the…
Comparative study of topological charge is performed. Topological charges are measured by a cloverleaf operator on smoothed gauge configurations. Various types of smoothing techniques are employed. Agreement of topological charges in…
The question of the dependence of the topological charge $q$ of a gauged Skyrmion, on the gauge field, is studied quantitatively. Two examples, both gauged with $SO(2)$ are studied and contrasted: i) The $O(3)$ model in $2+1$ dimensions,…
The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I…
We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topological quantum field theory in the sense of Atiyah.
Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms.…
We reconsider the detailed structure of the topological character of the instantons in pure Yang-Mills theory on $S^1\times\mathbb{R}^3$, so-called calorons. The claim is that the standard formula for the topological character, the second…
Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However,…
We introduce topological magnetic field in two-dimensional flat space, which admits a solution of scalar monopole that describes the nontrivial topology. In the Chern-Simons gauge field theory of anyons, we interpret the anyons as the…
In a somewhat overlooked work by Seiberg, a definition of the topological charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and L\"{u}schers charge definition are related up to the section of the bundle. With the…
It is well known that charges coupled to a pure Chern-Simons gauge field in (2+1) dimensions undergo an effective change of statistics, i.e., become anyons. We will consider several generalizations thereof, arising when the gauge field is…
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the…
The topological supersymmetry of the pure Chern-Simons model in three dimensions is established in the case where the theory is defined in the axial gauge.
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to…
We examine the thermal behavior of a relativistic anyon system, dynamically realized by coupling a charged massive spin-1 field to a Chern-Simons gauge field. We calculate the free energy (to the next leading order), from which all…
Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions. It is conjectured that…
We show that when a Chern-Simons term is added to the action of $SU(N)$ ($N\geq 3$) Yang-Mills theory in 5 dimensions the usual self-dual topological solitons present in the theory necessarily pick up a (topological) electric charge.