用模矩阵实验探索拓扑序及其破缺
Experimentally Probing Topological Order and Its Breakdown via Modular Matrices
摘要：
自20世纪80年代首次在分数量子霍尔系统中观察到拓扑有序态以来，物质相的现代概念经历了巨大的发展。在本文中，我们探讨的问题：有多少细节的物理拓扑秩序原则上可以观察到使用最先进的技术？我们发现，使用令人惊讶的少的数据，即复曲面代码哈密顿在存在的通用障碍和失谐从其确切的可解点，模块化矩阵-表征任意统计，是一些最基本的指纹的拓扑秩序-可以重建具有很好的精度仅通过实验手段。这是第一个实验实现这些基本签名的拓扑秩序，测试其鲁棒性对扰动，并证明了原则-目前的技术已经达到了精度，以确定物质的阶段，因此，探测相空间的扩展区域周围的可溶点之前，其故障。考虑到任意子统计在量子计算中的特殊作用，我们的工作在探测和实际利用这些奇异的物质相方面都有着无数的应用前景。
英文摘要：
The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much detail of the physics of topological orders can in principle be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices -- characterizing anyonic statistics that are some of the most fundamental finger prints of topological orders -- can be reconstructed with very good accuracy solely by experimental means. This is a first experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle -- that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.
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