The information convex in topological orders

Abstract

It is widely known that topological orders have long-range entangled gapped ground states from which nontrivial properties can be extracted. We introduce a new theoretical framework named the information convex, the (convex) set of reduced density matrices of a subsystem in its lowest energy, to characterize topological orders. (1) As a concrete example, we present the calculated topology dependent structure of information convex in the quantum double models and show it reveals properties of bulk anyons and deconfined topological excitations along a gapped boundary, and the condensation rules relating them. (2) As a step towards answering "why the structure of information convex looks that way and whether it has predictive power?" we look into some quantum informational constraints. The topological contribution to von Neumann entropy from each topological excitation type and certain fusion constraints are shown to emerge due to strong subadditivity, assuming fusion multiplicity is encoded in certain topological invariant manner.