Quenching Kinetics And Quantum Phase Transitions On XY Spin Chains

Quantum entanglement is one of the most important concepts in quantum physics.Recently,it is found that quantum entanglement is related to quantum phase transition closely.In the equilibrium state,there are much researches on quantum phase transition and quantum entanglement.In the non-equilibrium,the evolutionary behavior of quantum many-body spin systems is complex relatively.In recent years,the related research is less,especially the study of the relation between entangled dynamics and quantum phase transition(QPT)due to complexity.Recent advances in ultracold atom,molecule,and ion experiments and the development and application of ultrafast pulsed lasers to probe strongly correlated dynamics in solid-state systems have enabled the experimental study of dynamics in far-from-equilibrium quantum many-body systems.These experimental capabilities have stimulated some theoretical work,but the study of non-equilibrium evolution law in quantum many-body spin systems is in preliminary stage and a large body of basic problem need to be addressed.By applying quantum renormalization group method,it is studied that the relation between QPT and quench dynamics quantity of entanglement in the one dimensional anisotropic XY spin chains.The exchange coupling constants of this system along the x spin direction is non-negative number and along the y spin direction is non-positive number.The stable fixed point and unstable point is obtained by implementing the quantum renormalization group.Combined competition analysis,we obtain the system has three phases: antiferromagnetic Ising phase in the“x direction”,spin-fluid phase and ferromagnetic Ising phase in the “y direction”.Next,two kinds of quantum quench protocols are applied to initiate dynamics of the system.We adopt the concurrence to quantify the entanglement and study the evolution of concurrence when the anisotropic parameter and time are mutually fixed.When anisotropic parameter is fixed,the concurrence periodically fluctuate with time;When time is fixed,the concurrence show singular behavior near the critical point,which indicates QPT can be described by the concurrence in any time.We study the relation between evolution period and QPT further,and find that the evolution period show singular behavior near the critical point.In order to illustrate,first derivative of evolution period is study,and find it show divergence behavior closed to the critical point,which indicates that the transition is second-order QPT.Finally,the scaling of the system and critical exponent is obtained by calculate the relation between the minimum of the first derivative and the system size.