Study On Tensor Network In The Application Of Holographic Gravity And Its Numerical Method

Tensor networks provide a new tool for the study of the microstructure of spacetime.The main ideal is that spacetime could emerge from the boundary.That is very similar to the holographic principle which states that a d +1-dimensional gravity theory could be described by a d-dimensional non-gravity theory on the boundary.AdS/CFT duality,as an application of the holographic principle,has been extensively studied with the tensor networks.In this thesis,we starting with the tensor network formalism,we study its numerical method and applications.We also use the tensor networks to deduce the metric of spacetime.First,we numerically simulate the ground state of quantum Ising chain by using tensor networks.Then we use this ground state as a quantum channel to teleport the entangled Werner state.We show that the derivate of the fidelity as the measurement of the difference between input and output states with respect to the parameter in a quantum Ising chain exhibits a divergence at the critical point.Second,we use multiscale entanglement renormalization ansatz(MERA)to emerge the AdS spacetime.For a thermal CFT,the emerged spacetime is either a BTZ black hole or a thermal AdS.