On the emergence of gravitational dynamics from tensor networks

Abstract

Abstract Tensor networks are used to describe the ground state wavefunction of the quantum many-body system. Recently, it has been shown that a tensor network can generate the anti-de Sitter (AdS) geometry by using the entanglement renormalization approach, which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence. However, whether the dynamical connections can be found between the tensor network and 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.