title: Entanglement rates and area laws.
abstract: We prove an upper bound on the maximal rate at which a Hamiltonian interaction can generate entanglement in a bipartite system. The scaling of this bound as a function of the subsystem dimension on which the Hamiltonian acts nontrivially is optimal and is exponentially improved over previously known bounds. As an application, we show that a gapped quantum many-body spin system on an arbitrary lattice satisfies an area law for the entanglement entropy if and only if any other state with which it is adiabatically connected (i.e., any state in the same phase) also satisfies an area law.
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Karel
authors.initials: K
authors.lastname: Van Acoleyen
authors.forename: Michaël
authors.initials: M
authors.lastname: Mariën
authors.forename: Frank
authors.initials: F
authors.lastname: Verstraete