Southwest Quantum Information and Technology

Random tensor networks as models of holography

Presenting Author: Sepehr Nezami, Stanford Institute For Theoretical Physics
Contributing Author(s): Patrick Hayden, Xiao-Liang Qi, Nathaniel Thomas, Michael Walter, Zhao Yang

Ryu and Takayanagi proposed that if a conformal field theory (CFT) has a gravitational dual, then the entropy of a region in a CFT state is given by the area of a minimal surface in the dual gravitational theory. The author and collaborators show in [1] that the set of all possible entropies given by the Ryu-Takayanagi (RT) formula can be described by a graph model as follows: Consider an arbitrary graph G and split the set of vertices into the boundary (M) and bulk (B) vertices. Then the entropies are defined on the subsets of the boundary vertices A\in M and given by the weight of the minimum cut through the graph separating A and M-A. Following the graph model described in [1], we demonstrate that by lifting the graph to a tensor network with the same skeleton and contracting the bulk tensors, it is possible to induce a quantum state on the boundary vertices with the entropies prescribed by the graph model. Specifically, we prove that if we pick the tensors as random (either unitary Haar random or a random stabilizer tensor) the entropies will match the entropies of the graph model with high probability. Surprisingly, the random tensor model not only provides a simple manifestation of the entropies of the AdS/CFT duality, it also captures many other known properties of the duality and can be thought as a toy model for the duality itself. Some of these properties are the error correction properties, structure of the CFT spectrum, and the Hawking-Page transition. [1]The Holographic Entropy Cone

(Session 5 : Thursday from 5:00 - 7:00 pm)