Entanglement structures from modified IR geometry
arxiv(2024)
摘要
We investigate a new proposal connecting the geometry at various radial
scales in asymptotic AdS spacetime with entanglement structure at corresponding
real-space length scales of the boundary theory. With this proposal, the bulk
IR geometry encodes the long-scale entanglement structure of the dual quantum
system. We consider two distinct types of IR geometries, namely the spherical
case and the hyperbolic case, which are intimately related to the physics of
differential entropy and brane-world holography separately. We explore the
corresponding change in the dual long-scale entanglement structures, utilizing
the tools of the Ryu-Takayanagi formula, conditional mutual information, and
partial entanglement entropy. The results indicate that modifying the IR
geometry leads to a redistribution of entanglement at scales longer than a
critical length determined by the location of the IR region, with the two
modified IR geometries corresponding to two opposite ways of redistribution.
Furthermore, we establish the maximum amount of entanglement that can be
modified, which is proportional to the area of the IR region.
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