Quantum Coherence And Phase Transitions With A One-dimensional XY Spin Model Of Staggered DM Interactions

Quantum coherence is derived from the superposition principle of quantum states,it is a more fundamental quantum property than quantum entanglement and other non classical correlations and it plays an important role in many fields,such as quantum optics,quantum computing,quantum information and quantum biology.In recent years,with the quantitative framework for coherence,it has been found that coherence can describe the quantum critical properties of spin systems.In this thesis,the quantum coherence,quantum phase transition and quench dynamic evolution behavior of onedimensional XY model with staggered Dzyaloshinskii-Moriya(DM)interaction are studied by using quantum renormalization group theory.In this thesis,the quantum renormalization group method(Kadanoff block method)is used to study the one-dimensional XY model with interleaved DM interaction,and get the stable fixed point and unstable fixed point of the system are obtained,which respectively correspond to the spin liquid phase and the Néel phase of the system`s critical point of phase.Taking L1 normal form as the measure of quantum coherence,the expression of quantum coherence of three sites is answered by using the ground state density matrix,and the curves of quantum coherence of the system with anisotropic parameter and DM interaction at different scales are obtained respectively.When DM interaction is constant,the coherence of the system increases from a value less than 3 to a maximum value of 3,then decreases rapidly and tends to a constant value.With the increase of system scale,the range of anisotropy parameter corresponding to the maximum quantum coherence is larger.When the anisotropy parameter is constant,the coherent evolution behavior of the system is similar to that of DM interaction.The first order partial derivative of the coherence is also calculated and it is found that the non-analytical behavior of the system occurs at the critical point,which indicates the quantum phase transition.Then the relationship between the maximum value of the first partial derivative of the coherence and the scale of the system is obtained.In the second part of this thesis,we study the relationship between quenching dynamics and quantum phase transition,as well as the coherent evolution behavior at different scales.Using different quenching protocols,the system evolves with time at zero temperature,and the coherence evolution of different anisotropic parameters with time under different quenching protocols,the coherence evolution of different DM parameters with time,the evolution of coherence with time at different scales and the evolution of coherence with anisotropic parameters at a certain time at different scales is obtained.For different quenching protocols,the system evolves periodically with time,but the evolution behavior is inconsistent under the thermodynamic limit.It is also found that the coherence of the system has a singularity behavior at the critical point,which indicates that the quantum phase transition occurs at the critical point.