Quantum Discord And Quantum Phase Transition In Heisenberg Spin Chain

As an important part of modern physics, quantum information and computation develops rapidly in this year. Quantum correlation, which reflects the basic properties of the quantum world such as the quantum coherence, probability and nonlocality, plays a key role in this field. Recently, the study of quantum correlation in many-body systems has attracted many attention. In this paper, by using of the concept quantum discord (QD), we will study the quantum correlation of1-dimension Heisenberg chain and reveal the relation between QD and the eigenenergies. We focus on the strange phenomena of QD near the quantum phase transition point.This thesis comes in three part. The first part is Chapter1where we systematically introduce the background, including quantum entanglement, quantum phase transition(QPT) and QD.The second part includes Chapter2and Chapter3, where we discuss the quantum correlation in1-dimension Heisenberg chain with GMQD. In Chapter2, we will study the spin-1/2Heisenberg chain with next-nearest interaction, also called J1-J2model. The analytical result of GMQD and energy is given for small scale system, and only numerical results are given for large scale system. With the help of Feynman-Hellman rule, we reveal the connection between the GMQD and energy, and study the feature of quantum correlation at the QPT point. In Chapter3, we study the (1/2,1) mixed-spin Heisenberg chain. We obtained the analytical result of both GMQD and internal energy for2-particle system, and show their correlation. We also display the quantum entanglement measured by negativity, and demonstrate the relationship and difference between the quantum entanglement and quantum correlation. We still study the behavior of quantum correlation at the QPT point, and the effect of temperature is considered. The cases of large scale systems are studied numerically.In the third part, the conclusion will be given.