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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Additional details
- PMCID
- PMC6467278
- Eprint ID
- 79399
- Resolver ID
- CaltechAUTHORS:20170726-092004962
- Air Force Office of Scientific Research (AFOSR)
- Army Research Laboratory (ARL)
- Army Research Office (ARO)
- NSF Physics Frontiers Center
- Created
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2017-07-26Created from EPrint's datestamp field
- Updated
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2022-03-23Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter