Study On The Ground State And Dynamic Properties Of One-dimensional Long-range Bosons System

This thesis aims to use the density matrix renormalization group(D M R G)theory to investigate the ground state and dynamic properties of long-range quantum many-body systems.Our research is divided into two main aspects:First,we study the ground state properties of the one-dimensional Bose-Hubbard model with long-range hopping and even-odd imbalance potential wells,calculate its ground state phase diagram,and compare the changes in the ground state when long-range interactions are introduced.Second,based on the phase diagram,we investigate the time evolution of correlations,entanglement,and mutual information between different phases under long-range interactions to explore the impact of long-range correlations on information propagation.First,we use the density matrix renormalization group(D M R G)algorithm to calculate the ground state properties of the one-dimensional long-range BoseH ubbard model and investigate two special cases-full and half filling.In the case of full filling,we find that changing the size of the long-range hopping or evenodd imbalance potential wells can change the first-order phase transition between the Mott insulating state and the charge density wave state in the short-range system,resulting in a second-order phase transition between the Mott insulating state,super solid state,and charge density wave state in the long-range system.In the case of half filling,we find only a phase transition from super fluid to charge density wave.Based on the phase diagram,further we use the Time D ependent Variational Principle(TD VP)algorithm to investigate the time evolution of correlations,entanglement,and mutual information between different phases under long-range interactions.We find that under long-range interactions,the changes in correlations,entanglement,and mutual information between different phases have very different characteristics.In long-range quantum systems,the evolution of mutual information is often closely related to the evolution of entanglement.Since mutual information and entanglement are both quantum information measures that reflect the correlations between different subsystems in the system,they are closely related.In long-range quantum systems,the correlations between subsystems often exhibit long-range features,so the evolution of mutual information and entanglement often exhibit a non-local trend;at the same time,the evolution characteristics of mutual information and entanglement between different phases in long-range quantum systems will also be different.These findings provide new perspectives for understanding the ground state and dynamic properties of quantum many-body systems.Our research demonstrates the non-trivial physical behavior of many-body systems under long-range interactions,which contributes to a deeper understanding of ground state properties and phase transition phenomena.Our results not only provide new insights and challenges for quantum many-body systems in theory,but also provide guidance and inspiration for material design and quantum computing in practice.