Kato, Kohtaro and Brandão, Fernando G. S. L. (2019) Locality of Edge States and Entanglement Spectrum from Strong Subadditivity. Physical Review B, 99 (19). Art. No. 195124. ISSN 2469-9950. doi:10.1103/PhysRevB.99.195124. https://resolver.caltech.edu/CaltechAUTHORS:20180620-190843167
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Abstract
We consider two-dimensional states of matter satisfying a uniform area law for entanglement. We show that the topological entanglement entropy is equal to the minimum relative entropy distance from the reduced state to the set of thermal states of local models. The argument is based on strong subadditivity of quantum entropy. For states with zero topological entanglement entropy, in particular, the formula gives locality of the states at the boundary of a region as thermal states of local Hamiltonians. It also implies that the entanglement spectrum of a two-dimensional region is equal to the spectrum of a one-dimensional local thermal state on the boundary of the region.
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| Additional Information: | © 2019 American Physical Society. Received 24 May 2018; revised manuscript received 17 April 2019; published 14 May 2019. We thank Burak Sahinoglu for helpful discussions. We acknowledge support from the NSF. Part of this work was done when both of us were working in the QuArC group of Microsoft Research. K.K. acknowledges the Advanced Leading Graduate Course for Photon Science (ALPS) and JSPS KAKENHI Grant No. JP16J05374 for financial support. | |||||||||
| Group: | Institute for Quantum Information and Matter | |||||||||
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| Issue or Number: | 19 | |||||||||
| DOI: | 10.1103/PhysRevB.99.195124 | |||||||||
| Record Number: | CaltechAUTHORS:20180620-190843167 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180620-190843167 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 87288 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Joy Painter | |||||||||
| Deposited On: | 21 Jun 2018 16:07 | |||||||||
| Last Modified: | 15 Nov 2021 20:46 |
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