One-dimensional Topological Kondo Insulator:a Finite Temperature Study

In recent years,topological insulator that have both electronic correlation effects and non-trivial topological structures have become one of the hot topics in the research of condensed matter physics.Among them,topological Kondo insulator SmB₆is a typ-ical representative.Theoretically studying its basic physical properties often aided by simplified lattice models,such as topological Kondo lattice or periodic Anderson mod-els.At present,the ground states of these topological Kondo insulator models have been widely studied,but the basic physical characteristics of finite temperature topological Kondo insulator are still largely unknown.In this thesis,in order to further explore the electron strong correlation with the topological effect on topology Kondo insulator at finite temperature:we take a one-dimensional p-wave periodic Anderson model（simplified model of the topological Kon-do insulator）as an example to discuss the complex physical properties in topological Kondo insulator at finite temperature.Specifically,the first chapter introduces the basic concepts of topological insulator and Kondo insulator.In the second chapter,we will introduce the fundamental model of one-dimensional p-wave periodic Anderson model,and briefly introduce the quantum monte carlo simulation method.The third chapter,we give the derivation of some important physical quantities in the quantum monte car-lo simulation of zero-temperature projection and finite temperature determinant based on periodic Anderson model.In the fourth chapter,numerical simulation results and analysis are given.From the numerical simulation,we find that:1)The topological Haldane phase not only exists in the zero-temperature ground state,but the temperature dependence of the edge magnetization also indicates its existence in finite temperature systems.This indi-cates the stability of the gapful topological state to thermal fluctuations,which empha-sizes the robustness of the（symmetry-protected）topological order;2)The temperature-dependent spin structure factor and the static spin susceptibility show the existence of local magnetic moments at edge sites.The high temperature susceptibility exhibits a Curie-like behavior（the 1/T law）,and its low-temperature upturn behavior is similar to the experimental results of SmB₆at T<50K;3)The system has an energy scale T_cr,which represents a critical temperature at which the system enters a low temper-ature regime.When the temperature is lower than T_cr,the Kondo screening effect of the edge sites is very small,which can form a local magnetic moment.These findings confirm the stability of general topological states at finite temperatures and indicate that experimentally measurable spin susceptibility and spin structural factors can be used to characterize heavy fermion systems with Haldane topological states.