Holographic view on quantum correlations and mutual information between disjoint blocks of a quantum critical system
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Física AplicadaSponsors
Spanish Office for Science FIS2009-13483-C02-02, Fundación Séneca Región de Murcia 11920/PI/09 and the UPCT ”Programa de Movilidad”Publication date
2011-10Publisher
Journal of High Energy PhysicsBibliographic Citation
J.Molina-Vilaplana, P.Sodano (2011). Holographic view on Quantum Correlations and Mutual Information between disjoint blocks of a quantum critical system. Journal of High Energy Physics. 10, 21Peer review
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FísicaPhysics
Teoría cuántica
Quantum theory
Abstract
In (d + 1) dimensional Multiscale Entanglement Renormalization Ansatz
(MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic
geometry of Anti de Sitter space (AdSd+2) with the original system lying at the
boundary. We analyze the MERA renormalization flow that arises when computing the
quantum correlations between two disjoint blocks of a quantum critical system, to show
that the structure of the causal cones characteristic of MERA, requires a transition between
two different regimes attainable by changing the ratio between the size and the separation
of the two disjoint blocks. We argue that this transition in the MERA causal developments
of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual
information is computed using the Ryu-Takayanagi formula. As an explicit example, we
use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two
disjoint intervals of a one dimensional boundary ...
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