Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy

• URL: http://arxiv.org/abs/2110.01115v1
• Date: Sun, 3 Oct 2021 22:46:41 GMT
• Title: Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• Authors: Jonathan Lam, Yi-Zhuang You
• Abstract summary: Ryu-Takayanagi formula connects quantum entanglement and geometry. We propose a microscopic model by superimposing entanglement features of an ensemble of random tensor networks of different bond dimensions. We show mutual information can be mediated effectively by geometric fluctuation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Ryu-Takayanagi formula directly connects quantum entanglement and geometry. Yet the assumption of static geometry lead to an exponentially small mutual information between far-separated disjoint regions, which does not hold in many systems such as free fermion conformal field theories. In this work, we proposed a microscopic model by superimposing entanglement features of an ensemble of random tensor networks of different bond dimensions, which can be mapped to a statistical gravity model consisting of a massive scalar field on a fluctuating background geometry. We propose a machine-learning algorithm that recovers the underlying geometry fluctuation from multi-region entanglement entropy data by modeling the bulk geometry distribution via a generative neural network. To demonstrate its effectiveness, we tested the model on a free fermion system and showed mutual information can be mediated effectively by geometric fluctuation. Remarkably, locality emerged from the learned distribution of bulk geometries, pointing to a local statistical gravity theory in the holographic bulk.

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