论文标题
费尔米管和骨气性手性拓扑问题的内在标志问题
Intrinsic sign problem in fermionic and bosonic chiral topological matter
论文作者
论文摘要
臭名昭著的符号问题导致通用多体量子系统的蒙特卡洛模拟中的指数复杂性。然而，众所周知，许多物质阶段都可以接受无标志的代表，从而可以在古典计算机上进行有效的模拟。由多体物理学中长期存在的开放问题以及量子复杂性的基本问题所激发的，固有的符号问题的可能性（在物质阶段都承认没有任何无标志的代表者）最近被提出，但在很大程度上没有探索。在这里，我们确定了物质的一系列固有符号问题的存在。在此类中，我们排除了玻色子（或“ Qudits'）的杂种哈密顿人的可能性，以及用于费米子的无标志性蒙特卡洛算法的可能性。我们确定的本质上标志性问题类别的阶段是根据拓扑不变的，具有明显可观察的特征：手性中央电荷和Anyons的拓扑旋转。我们获得了自发性手性的相的类似结果，并提供了适用于手性和非手力拓扑问题的结果的证据。
The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. Here, we establish the existence of an intrinsic sign problem in a broad class of gapped, chiral, topological phases of matter. Within this class, we exclude the possibility of stoquastic Hamiltonians for bosons (or 'qudits'), and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The intrinsically sign-problematic class of phases we identify is defined in terms of topological invariants with clear observable signatures: the chiral central charge, and the topological spins of anyons. We obtain analogous results for phases that are spontaneously chiral, and present evidence for an extension of our results that applies to both chiral and non-chiral topological matter.
