Study On Correspondence Between Fabric Of Tensor Network And Geometry Of Asymptotic Anti-de Sitter Space-time

The development of black hole thermodynamics made people to realize that black hole whose temperature once was thought to be absolutely zero actually can radiate.J.Bekenstein pointed that the upper bound of entropy of the region is proportional to the area of it.Based on this,people get to know the holographic property of gravity.Holography principle originates from the universal property of black hole thermodynamics.It was first realized in Maldacena’s conjecture:AdS/CFT correspondence.Understanding the basic mechanism of AdS/CFT is of great importance in theoretical physics.AdS/CFT relates quantum gravity to many-body problem in condensed matter physics.Tensor network method which was invented to solve many-body problem may shed new light on our understanding of AdS/CFT.Motivated by above inspiration,in this thesis,we concentrate on emerging geometry from CFT based on tensor network method.By exploiting truncated MERA and surface/state correspondence,we find bulk geometry can naturally emerge from CFT.Moreover,some interesting phenomenon such as Hawking-Page phase transition can be easily described.Then,we investigate complexity,one basic property of tensor network,using quantum information theory.We find the equivalence between sub-region holographic complexity and fidelity susceptibility in field theory.At last,we generalize the study from tensor network to neural network and get the structure of geometry and entanglement of the neural network which describes the process of renormalization.We find that this structure matches the results in AdS/CFT.