Quantum Correlations Of A Hard-core Bose Gas In One-dimensional Optical Lattices

The determination and characterization of quantum phase transitions in strongly correlated many-body quantum systems has always been an important research topic in the frontiers of physics nowadays,and many important research results have emerged in this field.Disorder and disorder-induced quantum phase transitions are one of the hottest topics in this field.The famous Aubry-André Harper(AAH)model is a typical model to investigate this kind of disorder problem.It has an incommensurate lattice potential and is a quasi-periodic potential that can be used to mimick the true disorder in 1D tight binding systems.The generalized AAH model popularized on this basis has become an important research framework for studying the localization phenomenon of disorder induction and analyzing the topological properties.We mainly investigate hard core bose systems in one dimensional off-diagonal AAH lattice.Hard-core bose gase is an important kind of strongly correlated quantum many-body system.The so-called hard-core bose gas is a bose gas with strong repulsion interaction between particles,which requires that the bosons satisfy the hard core limit.Due to its unique properties,hard-core bose gas has attracted much attention since the 1960 s.In this thesis,we mainly investigate the ground state quantum correlation of hard core boson system in optical lattices and use it to determine and characterize quantum phase transitions of the ground state.In Chapter 2,based on a 1D diagonal AAH lattice model,we introduce the exact approach of one-dimensional hard core bose system in optical lattice from a very specific point of view.This exact approach is essentially a Bose-Fermi mapping,which based on the Holstein-Primakof transformation and the Jordan-Wigner transformation.Utilizing Bose-Fermi mapping,we can obtain the exact ground state of the system by using the properties of Slater determinant.Furthermore,as a simple practice and exercise,we introduce the noise correlation of hard core bosons in the one-dimensional diagonal AAH lattice model calculated by the above approach,and characterize the quantum phase transitions in the system.In Chapter 3,we investigate a hard core boson system in 1D off-diagonal AAH optical lattices,in which hopping term of the system is modulated by an additional incommensurate hopping term mimicking disorder.By using the exact numerical method introduced in Chapter 2,we obtain the exact ground state of the hard core boson system.By means of parallel numerical calculation,we obtain the momentum distribution and noise correlation of the system in different parameter regions.In addition,by means of detailed scaling analysis of the above quantum correlations,we can see that the scaling behavior of superfluid phase,critical point and bose glass phase is clear and different in this parameter region,and the system has two distinct ground state phases: superfluid phase and Bose glass phase.Finally,we compute derivatives of the central intensities of these quantum correlations with respect to the strength of the quasiperiodic disorder,and there are clear peak appears at the critical point.This provides a powerful signal that can be used to detect quantum phase transition induced by disorder experimentally.