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Machine learning statistical gravity from multi-region entanglement entropy
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DOI：10.1103/PhysRevResearch.3.043199.png)
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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 paper, 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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