Entanglement entropy quantifies how entangled a region of a many-body quantum system is with everything outside it. It is usually computed as the von Neumann entropy of the reduced density matrix obtained by tracing out the rest of the system, so a larger value means the region’s state cannot be described independently of its surroundings.
In two-dimensional gapped topological phases, the entanglement entropy of a disk-shaped region has a universal, size-independent correction on top of the expected boundary-length (“area law”) term — the topological entanglement entropy — which encodes global information about the phase’s anyon content. Combinations of entanglement entropies across overlapping regions, rather than a single region’s value, are what let quantities like the modular commutator extract further topological invariants, such as the chiral central charge, directly from a ground-state wave function.