Tensor networks for dynamic spacetimes

TL;DR

This paper extends tensor network models to dynamic spacetimes by redefining length via mutual information, enabling the calculation of boundary entropies in evolving geometries.

Contribution

It introduces a new length definition based on mutual information and demonstrates its use in a tensor network analogue of the maximin formula for dynamic spacetimes.

Findings

Mutual information-based length allows modeling of dynamic geometries.

The network analogue of the maximin formula computes boundary entropy.

The approach generalizes tensor networks beyond static spacetimes.

Abstract

Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.