44,086 research outputs found
Universal Wave Function Overlap and Universal Topological Data from Generic Gapped Ground States
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 should fully characterize the
topological orders with gapped or gapless boundary. For non-chiral topological
orders in 2+1D, this universal topological data consist of two matrices,
and , which generate a projective representation of on the
degenerate ground state Hilbert space on a torus. For topological orders with
gapped boundary in higher dimensions, this data constitutes a projective
representation of the mapping class group of closed spatial manifold
. For a set of simple models and perturbations in two dimensions, we show
that these quantities are protected to all orders in perturbation theory
Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant
We consider quantum holonomy of some three-dimensional general covariant
non-Abelian field theory in Landau gauge and confirm a previous result
partially proven. We show that quantum holonomy retains metric independence
after explicit gauge fixing and hence possesses the topological property of a
link invariant. We examine the generalized quantum holonomy defined on a
multi-component link and discuss its relation to a polynomial for the link.Comment: RevTex, 12 pages. The metric independence of path integral measure is
justified and the case of multi-component link is discussed in detail. To be
published in Physical Review
- …