Abstract
We prove that the entanglement entropy of any state evolved under an arbitrary long-range-interacting -dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any . We also prove that for any , the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.
- Received 25 March 2017
DOI:https://doi.org/10.1103/PhysRevLett.119.050501
© 2017 American Physical Society