Entanglement and Quantum Phase Transition in the Onedimensional Anisotropic XY Model 

Author  LiuShengZuo 
Tutor  KongXiangMu 
School  Qufu Normal University 
Course  Condensed Matter Physics 
Keywords  Quantum entanglement Quantum phase transitions XY model Quantum renormalization group 
CLC  O414.13 
Type  Master's thesis 
Year  2010 
Downloads  117 
Quotes  0 
Quantum entanglement is a strange and very complex pure quantum phenomena, has been widely used in quantum communication and information processing. Found in the study quantum phase transitions in condensed matter physics, quantum entanglement plays an important role, in which the concept of entanglement to describe the critical nature of the spin system. The thesis of onedimensional XY model with thermal entanglement and entanglement of zero temperature, the main contents are as follows: the Negativity definition of the DzyaloshinskiiMoriya (DM) interaction of spin and mixedspin XY model (1/2, 3/2) entanglement. By calculating the twoparticle entanglement between the degree of N, DM interaction can increase the degree of entanglement, and can spin reaches a stable value between 1 and mixedspin twoparticle entanglement degree. Exchange coupling between the spin interactions help to strengthen the thermal entanglement between the particles. When the exchange coupling interaction comparison hours, the concurrence of the system can be improved by strengthening the DM interaction, on the contrary, when the DM interaction is relatively small, the degree of entanglement can be improved by increasing the exchange coupling interaction. Temperature on the entanglement degree from the inhibitory effect, the higher the temperature, the smaller the degree of entanglement. When the temperature is higher, to make the thermal entanglement to reach a stable value you need stronger DM interaction. Under the same conditions, spin (s = 1) the entanglement between the two particles is less than the entanglement between two particles of the mixedspin. Quantum renormalization group method (s = 1/2) onedimensional anisotropic XY model quantum entanglement and quantum phase transitions. Concurrence (entanglement between blocks) as an order parameter to describe the critical properties of the system. Concurrence trend near the critical point, nonanalytical behavior and the scaling behavior. Coupling constant restructured several times iteration, concurrence at the critical point of the transition, and there were two stable value, these two values ??correspond to two different phases, namely the class of the Ising phase and spin liquid phase. For class Ising phase concurrence zero, indicating that the spin does not exist quantum correlations between the ordered arrangement. Spin liquid phase quantum fluctuations destroy the long program, quantum correlations between the spin. In order to analyze the critical nature of the system, we take the symbiotic entanglement immeasurable function number of Tsunatsune g (g = 1 y/1γ gamma for the anisotropy parameters). The maximum value of the first derivative of the concurrence between the logarithmic number system grid points a linear relationship, it shows the scaling behavior, and the position of the maximum of the first derivative of gmax with the system scale increases gradually close critical point, also shows the scaling behavior. To also found that system scale increases indefinitely, the concurrence first derivative is divergent at the critical point, the phase into the continuous phase transition occurred in the system.