论文标题
拓扑量子场理论中的内在符号问题
Intrinsic sign problems in topological quantum field theories
论文作者
论文摘要
标志问题是一个广泛的数值障碍，阻止我们模拟物理学最前沿的各种问题的平衡行为。侧重于此类问题的重要子类，Bosonic $（2+1）$ - 尺寸拓扑量子场理论，在这里，我们提供了一个简单的标准来诊断固有的符号问题 - 也就是说，该阶段固有的符号问题，无法通过任何本地单位转换来消除该阶段的问题。显式，\ textit {如果任何人激发的交换统计信息没有形成统一根的完整根集，则该模型具有内在的符号问题}。这在模块化$ S $和$ t $矩阵中包含的Anyons的统计数据之间建立了具体的联系，并在微观的哈密顿量中存在标志问题。此外，它在阶段上施加了限制，这是由杂质的哈密顿人所实现的。我们证明了这一点，并且是针对低能量的阿贝尔拓扑量子场理论所描述的一组大型间隙的骨化模型的更严格的标准，并提供了证据表明，它更普遍地适用于非亚洲和手性理论的类似结果。
The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behavior of various problems at the forefront of physics. Focusing on an important sub-class of such problems, bosonic $(2+1)$-dimensional topological quantum field theories, here we provide a simple criterion to diagnose intrinsic sign problems---that is, sign problems that are inherent to that phase of matter and cannot be removed by any local unitary transformation. Explicitly, \textit{if the exchange statistics of the anyonic excitations do not form complete sets of roots of unity, then the model has an intrinsic sign problem}. This establishes a concrete connection between the statistics of anyons, contained in the modular $S$ and $T$ matrices, and the presence of a sign problem in a microscopic Hamiltonian. Furthermore, it places constraints on the phases that can be realised by stoquastic Hamiltonians. We prove this and a more restrictive criterion for the large set of gapped bosonic models described by an abelian topological quantum field theory at low-energy, and offer evidence that it applies more generally with analogous results for non-abelian and chiral theories.
