01217nas a2200169 4500008004100000245006400041210006200105260001500167300001100182490000800193520070900201100001900910700002300929700003300952700002500985856003701010 2017 eng d00a{E}ntanglement area laws for long-range interacting systems0 aE ntanglement area laws for longrange interacting systems c2017/07/31 a0505010 v1193 a
We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α > D + 1. We also prove that for any α > 2D + 2, 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.
1 aGong, Zhe-Xuan1 aFoss-Feig, Michael1 aBrandão, Fernando, G. S. L.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1702.05368