Highly entangled spin chains and 2D quantum gravity
- URL: http://arxiv.org/abs/2005.00257v3
- Date: Mon, 1 Jun 2020 11:15:40 GMT
- Title: Highly entangled spin chains and 2D quantum gravity
- Authors: Fumihiko Sugino
- Abstract summary: Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume.
We introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Motzkin and Fredkin spin chains exhibit the extraordinary amount of
entanglement scaling as a square-root of the volume, which is beyond
logarithmic scaling in the ordinary critical systems. Intensive study of such
spin systems is urged to reveal novel features of quantum entanglement. As a
study of the systems from a different viewpoint, we introduce large-N matrix
models with so-called ABAB interactions, in which correlation functions
reproduce the entanglement scaling in tree and planar Feynman diagrams.
Including loop diagrams naturally defines an extension of the Motzkin and
Fredkin spin chains. Contribution from the whole loop effects at large N gives
the growth of the power of 3/2 (with logarithmic correction), further beyond
the square-root scaling. The loop contribution provides fluctuating
two-dimensional bulk geometry, and the enhancement of the entanglement is
understood as an effect of quantum gravity.
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