Topological entropy of realistic quantum Hall wave functions

The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.Comment: 6 pages, 6 figures; improved computations and graphics; added reference

Vector Graphics Complexes

International audienceBasic topological modeling, such as the ability to have several faces share a common edge, has been largely absent from vector graphics. We introduce the vector graphics complex (VGC) as a simple data structure to support fundamental topological modeling operations for vector graphics illustrations. The VGC can represent any arbitrary non-manifold topology as an immersion in the plane, unlike planar maps which can only represent embeddings. This allows for the direct representation of incidence relationships between objects and can therefore more faithfully capture the intended semantics of many illustrations, while at the same time keeping the geometric flexibility of stacking-based systems. We describe and implement a set of topological editing operations for the VGC, including glue, unglue, cut, and uncut. Our system maintains a global stacking order for all faces, edges, and vertices without requiring that components of an object reside together on a single layer. This allows for the coordinated editing of shared vertices and edges even for objects that have components distributed across multiple layers. We introduce VGC-specific methods that are tailored towards quickly achieving desired stacking orders for faces, edges, and vertices