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Published August 4, 2017 | Submitted + Published + Supplemental Material + Accepted Version
Journal Article Open

Entanglement area laws for long-range interacting systems

Abstract

We prove that the entanglement entropy of any state evolved under an arbitrary 1/r^α 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.

Additional Information

© 2017 American Physical Society. Received 25 March 2017; published 31 July 2017. We thank M. Hastings, G. Zhu, and R. Lundgren for helpful discussions. This work was supported by the AFOSR, NSF QIS, ARL CDQI, ARO MURI, ARO, NSF PFC at the JQI.

Attached Files

Published - PhysRevLett.119.050501.pdf

Accepted Version - nihms-1523684.pdf

Submitted - 1702.05368.pdf

Supplemental Material - supp2.pdf

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Created:
August 19, 2023
Modified:
October 26, 2023