Abstract
This thesis aims to explore the behavior of the ferromagnetic entanglement. Entanglement is an essential concept in quantum information science and the connection to many-body physics is recently enshrined. In particular the system of one-dimensional quantum critical chain and the corresponding conformal field theory (CFT) in the continuum limit. At first, we illustrate the idea by using spin-1 bi-linear bi-quadratic (BLBQ) model with SU(2) symmetry with periodic boundary condition. Then we design an approach to measure the effective central charge and the crossover length associated with the ferromagnetic entanglement. We applied the density matrix renormalization group (DMRG) method to obtain the ground state wave function and the entanglement. DMRG is invented by Prof. Steven R. White. It can address the problem of the exponential growth of the system size in the Hilbert space for the case of one-dimensional system. Finally we use the package called ``Matrix Product Toolkit’’ which was developed by Prof. Ian P. McCulloch to carry out the calculation.