Determining the structure of the real-space entanglement spectrum from approximate conditional independence
- Creators
- Kim, Isaac H.
Abstract
We study the ground state of a gapped quantum many-body system whose entanglement entropy S_A can be expressed as S_A=a|∂A|−γ, where a,γ are some constants and |∂A| is an area of the subsystem A. By using a recently proved operator extension of strong subadditivity of entropy [ I. H. Kim J. Math. Phys. 53 122204 (2012)], we show that a certain linear combination of the real-space entanglement spectrum has a small correlation with almost any local operator. Our result implies that there exists a structure relating the real-space entanglement spectrum over different subsystems. Further, this structure is inherited from the generic property of the ground state alone, suggesting that the locality of the entanglement spectrum may be attributed to the area law of entanglement entropy.
Additional Information
© 2013 American Physical Society. Received 9 October 2012; published 11 April 2013. This research was supported in part by NSF under Grant No. PHY-0803371, by ARO Grant No. W911NF-09-1-0442, and DOE Grant No. DE-FG03-92-ER40701. I would like to thank Alexei Kitaev for helpful discussions.Attached Files
Published - PhysRevB.87.155120.pdf
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Additional details
- Eprint ID
- 38412
- Resolver ID
- CaltechAUTHORS:20130510-085606203
- PHY-0803371
- NSF
- W911NF-09-1-0442
- Army Research Office (ARO)
- DE-FG03-92-ER40701
- Department of Energy (DOE)
- Created
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2013-05-10Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field