Dynamical Properties Of Quench Evolution In One Dimensional Topological Systems

Topological quantum phase transitions have attracted widely investigations since the Kosterlitz–Thouless transition has been discovered in 1970 s.In recent years,topological properties in equilibrium quantum systems have been deeply studied,while the study of non-equilibrium process is lacked and one important method to reveal the topological properties is the investigation of non-equilibrium quantum systems.The topology quantum systems have also been considered in the development of quantum information theory for their robust features in the present of environments,which also motivated the study of the non-equilibrium evolution process.In this thesis,we mainly studied the topological expression of the dynamical topological invariant in the one-dimensional p-wave Kitaev chain as well as the extended SSH model in the quenching evolution process.After quenching the topological systems with different topological states,we have studied the dynamical topological invariant and discussed its properties and the relation to the topological properties of the system,and also discussed the geometric meaning of some related quantities in the non-equilibrium evolution.In the first chapter,we have introduced the basic knowledge,including the topological properties of physical systems,the topological invariants,as well as the classification of topological systems based on their symmetries.In the second chapter,we have mainly introduced some topological models and their properties,such as the one-dimensional SSH model,the onedimensional p wave Kitaev chain,the corresponding topological phase diagrams are illustrated and then derived the general formula of quantum quenching evolution for two band quantum systems.In the third chapter,we have introduced the definition of dynamical topological invariants and geometric explanation,and then studied the quantum quenching process in the onedimensional p wave Kitaev chain,and the one dimensional extend SSH model.We have obtained the change of topological invariant during quenching between different topological phases,and proposed the geometric interpretation of dynamical topological invariants.In the last chapter,we summarized our studies.The studies on this thesis will benefit for the further investigation of topological quantum phase transitions.