Abstract
We study the ground state of a gapped quantum many-body system whose entanglement entropy can be expressed as , where are some constants and is an area of the subsystem . 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.
- Received 9 October 2012
DOI:https://doi.org/10.1103/PhysRevB.87.155120
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