title: Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States.
abstract: 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.
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Heidar
authors.initials: H
authors.lastname: Moradi
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.|Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Xiao-Gang
authors.initials: XG
authors.lastname: Wen