Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy

TL;DR

This paper introduces a machine learning approach to infer fluctuating bulk geometries from multi-region entanglement entropy data, demonstrating how local statistical gravity emerges in free fermion systems.

Contribution

It develops a generative neural network model that captures bulk geometry fluctuations from entanglement data, bridging quantum entanglement and statistical gravity.

Findings

Mutual information mediated by geometric fluctuations in free fermion systems.

Locality emerges from the learned bulk geometry distribution.

The model effectively recovers geometry fluctuations from entanglement entropy data.

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.