Machine learning statistical gravity from multiregion entanglement entropy
Abstract
The RyuTakayanagi formula directly connects quantum entanglement and geometry. Yet the assumption of static geometry lead to an exponentially small mutual information between farseparated 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 machinelearning algorithm that recovers the underlying geometry fluctuation from multiregion 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.
 Publication:

Physical Review Research
 Pub Date:
 December 2021
 DOI:
 10.1103/PhysRevResearch.3.043199
 arXiv:
 arXiv:2110.01115
 Bibcode:
 2021PhRvR...3d3199L
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 10 pages, 10 figures