Quantum Renormalization Group Approach To Study The Quantum Coherent,Multipartite Entanglement And Quantum Phase Transition In 2D And 3D Ising Model Under Transverse Field

Quantum information is a new inter-discipline about the quantum mechanics and information science.Over the last few decades,quantum information made great breakthroughs in both theoretical and experimental researches.Especially in recent years quantum coherence,quantum entanglement and trace distance emerged from quantum information science have been used to characterize quantum phase transition and obtained many valuable results.At the same time,quantum phase transition has been a hot topic and attracted much attention from condensed matter over past years.Many examples in the QPT such as spin-1/2 XY chain model?Ising model and Heisenberg model have been investigated thoroughly.Ising model as a kind of quantum spin system have been connected with quantum information theory and condensed matter physics.Although quantum phase transition(QPT)have been studied thoroughly in the condensed matter physics,it was only described in the framework of order parameter and symmetry breaking within the Landau-Ginzburg paradigm traditionally.In this thesis,we mainly pay attention to the problem from the quantum information perspective and study the QPT in 2D and 3D Ising model under transverse field.The results show that both the quantum coherence and multipartite entanglement are reliable tools to characterize and determine the critical points in many-body system.Moreover,both of them give rise to the same quantum critical points in whatever 2D or 3D Ising model under transverse field.In this paper,we adopt the real-space renormalization group approach to study the behaviors of 2D and 3D Ising model under transverse field near the critical points.It is found that the quantum coherence and multipartite of 2D and 3D Ising model under transverse field near the critical points exhibit some kind of sudden jumps phenomena.Besides,we also investigated the first partial derivative of quantum coherence of Ising model under transverse field near the critical point,and the results show that they exhibit some kind of singular behaviors as well.Our results obtained in this paper are the generalization of one dimensional spin chain by applying renormalization group method.We obtain the precise recurrence formulas related to the coupling constants of the Hamiltonian of the spin system,and therefore calculate the holistic quantum coherence and multipartite entanglement in many-body systems.