Quantum Phase Transition Of A Hard-core Boson Gas In One-dimensional Disordered Optical Lattices

Ultracold atoms are atoms that are at very low temperatures,and this temperature is generally close to absolute zero.Experimentally,ultracold atomic systems are often confined to various external potential fields such as optical lattices to study their physical properties.Due to the development of experimental technologies such as modern quantum optics,these systems have good controllability and diversity and can be used to simulate very idealized models.The ultracold atomic system in the optical lattice has become a very important and effective platform for studying the basic physical phenomena such as quantum phase transitions.For example,it is often used to study superfluid,BCS-to-BEC crossover,and so on.At present,many methods have been found experimentally to introduce disorder into the optical lattice,and the phenomenon of Anderson localization in matter waves has been observed.Therefore,the study of disorder and impurity effects based on the ultracold atomic system on the optical lattice platform has gradually become a hot topic in both theoretical and experimental research.There are many ways to realize disorder in the optical lattice.For example,disorder can be introduced in by superimposing an incommensurate sub-lattice on a main lattice,or by shining various exotic speckle patterns on an ultracold atomic gas,and it is also possible to load another relatively heavy atoms onto optical lattice to realize disorder and so on.The physical properties of the ultracold atoms in the incommensurate optical lattice can be described by the Aubry-André(AA)model.Based on this model,it was found that with the increase of the disorder strength,the ground state of the system will undergo a quantum phase transition from superfluid to Bose-glass phase.The Aubry-André(AA)model has gradually been studied extensively,and many variants of the model emerged.One of the most interesting is the off-diagonal Aubry-André(AA)model.In this thesis,wefocus on the physical properties of the one-dimensional hard-core Bose gas loaded into the off-diagonal Aubry-André(AA)model.Ultracold hard-core boson gas is an ultracold Bose atomic gas in which the interaction between bosons tends to be infinite.This is a very ideal extreme situation,usually only theoretically studied.However,the magic is that with Feshbach resonance and other means,this interesting physical system was actually implemented experimentally with the ultracold atomic system.In this thesis,we first introduced the exact numerical method for the treatment of hard-core boson gases in lattices.Then,based on this technique,some of the existing results of the Aubry-André(AA)model are repeated.Next,we focus on the quantum phase transition of ultracold hard-core Bose gas in one-dimensional off-diagonal disordered optical lattices.We mainly analyze the influence of off-diagonal disorder on the ground state properties of hard-core boson gases.Based on the off-diagonal Aubry-André(AA)model,using the rigorous numerical calculation methods introduced in the previous section,we calculate the many-body ground state wave function for the hard-core boson gas,and calculate the physical quantities of the system such as the superfluid factor and the correlation functions.It is found that with the increase of off-diagonal disorder strength,the quantum phase transition from superfluid state to Bose glass phase also occurs in the system ground state.However,in contrast to diagonal disorder,off-diagonal disorder can lead to Bose glass phase transition in a faster way.