Determining the structure of real-space entanglement spectrum from approximate conditional independence

Abstract

We study the ground state of a gapped quantum many-body system whose entanglement entropy $S_A$ can be expressed as $S_A=a|\partial A|-\gamma$, where $a,\gamma$ are some constants and $|\partial A|$ 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 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.

5 pages, 3 figures, added references. The conjecture in the original manuscript is now a theorem, see 1210.5190 . The new version reflects this change

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Cited by in corpus (8)

• Renyi generalizations of the conditional quantum mutual information
• Renormalization group constructions of topological quantum liquids and beyond
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Quantum Approximate Markov Chains are Thermal
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• A lower bound of quantum conditional mutual information
• Operator extension of strong subadditivity of entropy
• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity