The Study On The Properties Of Quasi-particles In Correlated Boson Systems

Recent advances in experimental and theoretical research on quantum degenerate gases have provided an unprecedented opportunity to simulate strongly correlated electronic systems in optical lattices.This quantum simulation will help solve some long-standing problems in condensed matter physics,such as the origin of quantum magnetism and the nature of high-temperature superconductivity that have plagued researchers for more than two decades.Since 1985,using laser cooling technique to trap atoms have been achieved,and in 1995 the Bose-Einstein condensation phenomenon was successfully observed.Ultra-cold atomic physics unveils a new chapter in physics and is a vane of new research directions in physics.With continuous research on cold atoms,the quantum degeneracy of Fermi gas and molecular gas are gradually realized,and a series of achievements have become milestones in the development of physics.Because various parameters in the ultracold atomic system can be precisely tuned,ultra-cold atoms are used to study BEC,superfluid,many-body systems,quantum information,quantum magnetism,etc.These studies have great impact on univeiling quantum phase transitions,and have wide application prospect.Based on the view of current research progress,we mainly study the properties of quasiparticle excitations in correlated boson systems.The main part of this thesis includes following three aspects: First,we briefly review the cold atom system,research methods and important models.Secondly,based on the cold atomic system,by using the tunable interaction between particles we apply the Landau phase transition theory to study the novel quantum states in the Bose-Hubbard model.It is found that when the in-situ repulsion interaction doesnot depend on the position of the lattice site,the system has a uniform superfluid phase and Mott insulator phases;when the interaction strength depends on the sublattice,the system has a(modulated)super-flow phase,density wave phases,Mott insulator phases.In order to further understand the topological properties of quasiparticle excitation in each phase,the properties of quasiparticle excitation of superfluid phase under weak interaction are studied by Bogoliubov theory.The path integral method is used to derive the quasiparticle excitation spectrum of the Mott insulator phases under strong interaction.It is found that the quasi-particle excitations in these phases has nontrivial topology and its topological properties are intrinsically related to the Bloch band topology.This study has deepened the understanding of the quasiparticle excitations that could have topological properties in correlated boson systems.