We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting anyons of Ising type, and the k=2 NASS (non-Abelian spin-singlet) state, supporting anyons of Fibonacci type. It is shown that the interface supports neutral excitations described by a 1+1 dimensional conformal field theory with central charge c=7/10. We discuss effects of the mismatch of the quantum statistical properties of the quasi-holes between the two sides, as reflected by the interface theory.
The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $τ$, with fusion rule $τ\timesτ=1+τ$. While it has been proposed that the anyon spectrum of the $ν=12/5$ fractional quantum Hall state includes a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a quantum Hall system has been lacking. Here we use recently proposed non-Abelian dualities to construct a Fibonacci state of bosons at filling $ν=2$ starting from a trilayer of integer quantum Hall states. Our parent t…
Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one di…
Experimental Evidence of Fractional Entropy in Critical Kondo Systems
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Centre de Nanosciences et de Nanotechnologies（纳米科学与纳米技术中心）；University College Dublin（都柏林大学学院）；Centre for Quantum Engineering, Science, and Technology（量子工程、科学与技术中心）；Université Paris Cité（巴黎西岱大学）
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max-Planck-Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian anyonic statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest neigh…
Exploiting Geometric Degrees of Freedom in Topological Quantum Computing
在拓扑量子计算机中，（2+1）维时空中的非阿贝尔任意子的辫子形成了量子门，其容错性依赖于辫子的拓扑性质，而不是几何性质。在这里，我们建议创建和利用冗余的几何自由度，以提高拓扑单量子位和双量子位量子门的理论精度。我们证明了力量的想法使用明确的结构在斐波那契模型。我们将其效率与Solovay-Kitaev算法进行了比较，并解释了其与早期构造中泄漏误差减少的关系[Phys. Rev. A 78，042325（2008）]。
