相关论文: Ising anyons in the $SU(2)_2$ Chern--Simons theory
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
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 give the complete set of irreducible representations of U(SU(2))_q when q is a m-th root of unity. In particular we show that their dimensions are less or equal to m. Some of them are not highest weight representations.
The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie…
A U(N) Chern-Simons theory on noncommutative $\mathbb{R}^{3}$ is constructed as a $\q$-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that…
We provide a mathematical definition of a low energy scaling limit of a sequence of general non-relativistic quantum theories in any dimension, and apply our formalism to anyonic chains. We formulate Conjecture 4.3 on conditions when a…
It is shown that a recent claim of equivalence between three Chern-Simons theories is not tenable.
We continue our investigation of the quantum equivalence between commutative and noncommutative Chern-Simons theories by computing the complete set of two-loop quantum corrections to the correlation function of a pure open Wilson line and…
A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for such a functional in appropriate function spaces to prove…
We reinterpret U(N) Chern-Simons-Witten theory quantized on a torus as a free fermion system. Its Hilbert space and some observables are simply related to those of group quantum mechanics, even at finite N and k. Its large N limit can be…
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…
We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…
We present an improved study of spectroscopic observables in the $SU(2)$ Yang-Mills theory with two adjoint fermions. We make an improvement on the precision of previous results which clarify the scale of finite volume effects present. This…
We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the $SU(N)_k \times SU(M)_{-k}$ gauge group. At small but fixed $M \ll N$, this system approaches the…
Here, we provide a simple Hubbard-like model of spin-$1/2$ fermions that gives rise to the SU(2) symmetric Thirring model that is equivalent, in the low-energy limit, to Yang-Mills-Chern-Simons model. First, we identify the regime that…
In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show…
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…
Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by…
In this article, we will compute the expectation value of observables (which appear as Wilson loops) in $\mathrm{U}(1)^n$ Chern-Simons theory for closed oriented $3$-manifolds. We will show how the various topological sectors of the…
The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern-Simons theory, which yields the so-called $\rm{SU}(2)_k$ anyon models that often appear in the context of…