Oral: Geometric Additivity of Modular Commutator for Multipartite Entanglement

A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. In this talk, we present novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, indicating that a modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. We illustrate the bulk and edge subsystems that manifest the geometric additivity. We also discuss the geometric aspects of entanglement based on numerical calculations and a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories.