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Entanglement area laws for long-range interacting systems

Gong, Zhe-Xuan and Foss-Feig, Michael and Brandão, Fernando G. S. L. and Gorshkov, Alexey V. (2017) Entanglement area laws for long-range interacting systems. Physical Review Letters, 119 (5). Art. No. 050501. ISSN 0031-9007. PMCID PMC6467278. http://resolver.caltech.edu/CaltechAUTHORS:20170726-092004962

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.119.050501DOIArticle
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467278PubMed CentralArticle
https://arxiv.org/abs/1702.05368arXivDiscussion Paper
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
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.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Army Research Laboratory (ARL)UNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Classification Code:PACS numbers: 03.65.Ud, 03.67.Bg, 75.10.Dg
PubMed Central ID:PMC6467278
Record Number:CaltechAUTHORS:20170726-092004962
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170726-092004962
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79399
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Jul 2017 16:27
Last Modified:18 Apr 2019 18:20

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