Theory of Fractional Statistics

在这项新的研究工作中，将对分数统计粒子(任意子)进行几项数值研究。分数统计伴随着二维粒子数的分数细化而产生；它已被证明出现在分数量子霍尔效应中，也可能出现在高温超导体中。将开发和测试分数统计的随机抽样(蒙特卡罗)算法。这项工作是此类工作中的第一项，应该会大大提高我们处理多任意子问题的能力。对任意子的精确对角化技术的研究将继续下去。特别是，我们将考察任意子屏蔽带电杂质所产生的磁矩；未微扰系统中自发磁矩的温度依赖性；以及零场中任意子的霍尔电导。服从分数统计的粒子可能与分数量子霍尔效应和高温超导电性有关的发现，重新引起了人们对这些被称为任意子的奇怪粒子的兴趣。这些粒子是二维空间独有的，具有与更传统的玻色子和费米子不同的性质。虽然任意子具有基本的理论意义，但它们与高温超导体的可能关联已经刺激了人们对它们在这些二维材料中的作用进行实验验证的探索。

On this new research effort several numerical studies will be undertaken on particles with fractional statistics (anyons). Fractional statistics arise in connection with particle number fractionalization in two dimensions; it has been shown to occur in the fractional quantum Hall effect, and may also occur in the high temperature superconductors. A stochastic sampling (Monte Carlo) algorithm for fractional statistics will be developed and tested. This work is the first of its kind and should substantially enhance our ability to treat the many-anyon problem. Studies of exact diagonalization techniques for anyons will continue. In particular, we will examine the magnetic moment arising from the screening by anyons of a charged impurity; the temperature dependence of the spontaneous magnetic moment in the unperturbed system; and the Hall conductance of anyons in zero field. %%% The discovery of the possible relevance of particles obeying fractional statistics to the fractional quantum Hall effect and high temperature superconductivity has renewed interest in these strange particles called anyons. These particles are unique to two-dimensional space and possess properties different than the more conventional bosons and fermions. While anyons are of fundamental theoretical interest, their possible relevance to high temperature superconductors has stimulated searches for experimental verification of their role in these two-dimensional materials.