On the emergence of gravitational dynamics from tensor networks

TL;DR

This paper proposes that gravitational dynamics can emerge from tensor networks by linking their wave functions, satisfying the Wheeler-DeWitt equation, to quantum gravity and holography, bridging tensor network models and gravitational theories.

Contribution

It introduces a novel framework connecting tensor networks with gravitational dynamics through the Wheeler-DeWitt equation and holographic principles.

Findings

Tensor networks can generate AdS geometry via entanglement renormalization.

Gravitational dynamics emerge if tensor network wave functions satisfy the Wheeler-DeWitt equation.

The approach bridges tensor networks with quantum gravity and holography.

Abstract

Tensor networks are powerful techniques that widely used in condensed matter physics. In this language, the wave function of a quantum manybody system is described by a network of tensors with specific entanglement structures. Recently, it is shown that tensor network can generate the anti-de Sitter (AdS) geometry by using the entanglement renormalization approach. However, whether the dynamical connections can be found between the tensor network and the gravity is an important unsolved problem. In this paper, we give a novel proposal to integrate ideas from tensor networks, entanglement entropy, canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler-DeWitt equation.