论文标题
从单个散装基态提取威尔逊循环操作员和分数统计数据
Extracting Wilson loop operators and fractional statistics from a single bulk ground state
论文作者
论文摘要
物质拓扑阶段的一个基本方面是，威尔逊环路运营商的存在，这些操作员保持基础状态子空间不变。在这里，我们介绍并实现了一个公正的\ rm数值优化方案，以系统地找到Wilson Loop操作员给定磁盘上一个凹陷的Hamiltonian的单个基态波函数。然后，我们展示如何通过进一步的优化将这些威尔逊循环操作员切割和胶合，从而为可以创建，移动和消灭任何激励的操作员提供。随后，我们使用这些操作员来确定Anyons的编织统计数据和拓扑曲折，从而产生了一种从单波函数中完全提取拓扑顺序的方法。我们将我们的方法应用于扰动的复曲面代码的基础状态，并将半模型加倍，其磁场最高为临界值的一半。从当代的角度来看，这可以将其视为一种机器学习方法，以发现基态波函数的新兴1形形式对称性。从应用程序的角度来看，我们的方法与当前量子模拟器中的Wilson Loop操作员有关。
An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an \it unbiased \rm numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.
