Entanglement Entropy And Entanglement Distribution In Quantum Many-body System

This paper mainly focuses on two aspects.First we study the finite size effect of entanglement entropy(α-Renyi entropy)and its physical meaning based on XY model,then extend to multi-block entanglement entropy.We briefly review some properties of Shannon entropy and mutual information,then we use these properties to entanglement entropy(α-Renyi entropy).Next,we show the analytical calculation method of entanglement entropy,and discuss the finite size effect of the system in the gapless and the gapped phase respectively.Then we calculate the finite size effect of the multi-block discrete system with uniform expansion,and its critical behavior is similar to that of the single block system.Next,based on the one-dimensional Kitaev model,we introduce the long-range interaction to study the mechanism of long-range entanglement and the entanglement distribution.We show that the short-range interaction lattice model can not produce long-range entanglement.Based on the one-dimensional Kitaev model,we introduces the long-range interaction and discusses the conditions of long-range entanglement.We study the distribution of entanglement on the system lattice,discuss the boundedness of entanglement with CKW inequality.Finally,we study the singular properties of entanglement entropy and entanglement near the quantum phase transition point.