Study On Dynamic Localization Of One-dimensional Electron-phonon Coupling System

We have built a one-dimensional Peierls model with a non-adiabatic dynamics method to investigate the localization of electron.By considering two completely different lattice configurations of order and disorder,and discussing the two cases of no electron-electron interaction and having electron-electron interaction respectively,we have calculated the time evolution of charge density,entanglement entropy and OTOC in different environments,thus the dynamic evolution laws of the electron are obtained.In the first chapter,we briefly introduce the historical process and current situation of the study about carrier localization;Then the relative contents of polyacetylene and SSH model are explained in detail;Finally,we expound the main research contents in our paper and the significance of the research.In the second chapter,we describe the work carried out in the literature;Then introduce the model that we use and the relevant calculation methods;Finally we explain the definitions of the physical quantities to be calculated.In the third chapter,we discuss the case of zero temperature.There is no random thermal motion in the lattice,so the system is disorder-free.We select a "domain-wall" initial condition for lattice deformations and the electron is initially localized in the middle of the chain.It is found that when there is no interaction between the electrons,the electronic wavepacket will oscillate periodically,and the higher the lattice vibration frequency is,the smaller the localization length of the wavepacket will be.By calculating the entanglement entropies and OTOC,we can conclude that the type of localization in the system is dynamic localization.In addition,the strength of electron-electron interaction have a very important effect on the dynamic evolution of electrons.When the interaction is small enough,the electronic wavepacket can still oscillate back and forth,but its shape is affected to a certain extent;When the interaction is large,the oscillation of the wavepacket almost disappears;However,when the interaction is huge,the electron will be localized in the middle of the chain for a long time,and the system is in the Mott insulator phase.After adding the electron-electron interaction,the localization type of the electron does not change.In the fourth chapter,we discuss the case of finite temperature.In this case,disorder exists in the lattice which is caused by thermal motion.Two sets of random numbers with Gaussian distribution are selected as the initial conditions for the lattice deformations and their first derivatives respectively.The initial state of the electron is one of its energy eigenstates,and the electron is localized.We find that the periodic oscillation of the electronic wavepacket completely disappears and the electron will spread out from the middle along the one-dimensional chain.The higher the temperature is,the faster the electron diffuses.By calculating the OTOC,we can know that the localization type in the system mainly becomes to Anderson localization.After adding moderate interaction,the electron still spreads out from the middle all the time,but there is no obvious rule between the diffusion speed and temperature.At this time,the main localization type in the system is still Anderson localization,but there may be a certain degree of many-body localization effect.The localization of the electron will affect its transport property.In this paper,we observe a dynamic phase transition of localization types during the transition from zero temperature to finite temperature.