论文标题
非亚伯式的Anyon Gas中的交换和排除
Exchange and exclusion in the non-abelian anyon gas
论文作者
论文摘要
我们审查并发展了理想AYON的多体频谱理论，即平面中相同的量子粒子，其交换规则受$ N $ strands上的辫子组的单一表示控制。允许任意等级（取决于$ n $）和非亚洲代表，并让$ n \ to \ infty $，这定义了理想的非亚伯利亚多种气体。我们计算由融合代数定义的通用和广泛表示形式的交换运算符和阶段，包括斐波那契和伊斯丁模型。此外，我们扩展了统计排斥的方法（Poincaré和Hardy不平等）和局部排除原则（也暗示为Abelian Anyons开发的Lieb-Thrir-Thrirentrent Ristequality），以进行任意几何模型，即，与Braid Group的Unitary Arnity of Braid septionals of Braid sectherations notive andynynynynynys交换。
We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on $N$ strands. Allowing for arbitrary rank (dependent on $N$) and non-abelian representations, and letting $N \to \infty$, this defines the ideal non-abelian many-anyon gas. We compute exchange operators and phases for a common and wide class of representations defined by fusion algebras, including the Fibonacci and Ising anyon models. Furthermore, we extend methods of statistical repulsion (Poincaré and Hardy inequalities) and a local exclusion principle (also implying a Lieb-Thirring inequality) developed for abelian anyons to arbitrary geometric anyon models, i.e. arbitrary sequences of unitary representations of the braid group, for which two-anyon exchange is nontrivial.
