论文标题
从单波函数中提取多体Chern号
Extraction of many-body Chern number from a single wave function
论文作者
论文摘要
整数和分数量子大厅（IQH和FQH）状态的量化霍尔电导率与拓扑不变的多体Chern数直接相关。相互作用系统中这种不变的常规计算需要由扭角参数参数的多体波函数的家族，以计算浆果曲率。在本文中，我们演示了如何在不了解哈密顿量的情况下提取Chern数字的情况下提取Chern号。对于FQH状态，我们的方法需要一个额外的整数不变，作为输入：必须插入$2π$ flux量子的$2π$ flux量子，以获得拓扑上的琐碎激发。正如我们所讨论的那样，$ s $原则上可以从圆锥形上的基态波函数中获得，而无需对哈密顿式的知识。我们执行涉及IQH和FQH状态的广泛数值模拟来验证这些方法。
The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles in order to calculate the Berry curvature. In this paper, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian. For FQH states, our method requires one additional integer invariant as input: the number of $2π$ flux quanta, $s$, that must be inserted to obtain a topologically trivial excitation. As we discuss, $s$ can be obtained in principle from the degenerate set of ground state wave functions on the torus, without knowledge of the Hamiltonian. We perform extensive numerical simulations involving IQH and FQH states to validate these methods.
