Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2015 Jul 17;115(3):036802. doi: 10.1103/PhysRevLett.115.036802. Epub 2015 Jul 14.
We propose a way-universal wave-function overlap-to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M^{d}) of closed spatial manifold M^{d}. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations.
我们提出了一种通用的波函数重叠方法，从任何维度的有能隙系统的一般基态中提取通用拓扑数据。这些提取的拓扑数据可能完全描述了具有有能隙或无能隙边界的拓扑序。对于（2+1）D 中的非手性拓扑序，这些通用拓扑数据由两个矩阵 S 和 T 组成，它们在环面上的简并基态 Hilbert 空间上生成 SL(2,Z)的射影表示。对于高维中有能隙边界的拓扑序，这些数据构成了闭空间流形 M^{d}的映射类群 MCG(M^{d})的射影表示。对于二维中的一组简单模型和微扰，我们表明这些量在微扰论中是完全保护的。这些重叠为拓扑纠缠熵提供了一个更强大的替代方法，并允许更有效的数值实现。
