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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Cluster algebraic description of entanglement patterns for the BTZ black hole

arXiv
Authors: Bercel Boldis, Péter Lévay

Year

2021

Paper ID

62144

Status

Preprint

Abstract Read

~2 min

Abstract Words

122

Citations

N/A

Abstract

We study the thermal state of a two dimensional conformal field theory which is dual to the static BTZ black hole in the high temperature limit. After partitioning the boundary of the static BTZ slice into N subsystems we show that there is an underlying CN-1 cluster algebra encoding entanglement patterns of the thermal state. We also demonstrate that the polytope encapsulating such patterns in a geometric manner for a fixed N is the cyclohedron {mathcal C}N-1. Alternatively these patterns of entanglement can be represented in the space of geodesics (kinematic space) in terms of a Zamolodchikov Y-system of CN-1 type. The boundary condition for such an Y-system is featuring the entropy of the BTZ black hole.

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  • This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
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  • We study the thermal state of a two dimensional conformal field theory which is dual to the static BTZ black hole in the high temperature limit.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2108.10638 [2] arXiv https://arxiv.org/abs/2108.10638 [3] Publisher https://arxiv.org/abs/2108.10638

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