Anyon And Trimer Superfluid On A One-Dimensional Optical Lattice

We systematically study the anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint.We analyze the effect of an induced hardcore constraint in the pseudo-fermion limit at statistical angles ???,which leads to the stabilization of superfluid ground state for vanishing or even small attractive on-site interactions.For finite statistical angles,we study the non-conventional broken-symmetry superfluid peaked at a nonzero momentum,resulting in an interesting beat phenomenon of single particle correlation functions.In particular for ????,we observe a wealth of exotic properties including a first order transition between different superfluid phases and a two-component partially paired phase for large fillings without the need of an additional three-body hardcore constraint.Furthermore,the Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = O,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A 81,011601(R)(2010)]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.The main content of this thesis is arranged as follows:In the first chapter,we introduce the background knowledge and theoretical basis of quantum phase transition,anyon and trimer superfluid,and show the corresponding Hamiltonian.In the second chapter,we mainly introduce the simulation and analysis methods for the anyon Hubbard model and the Bose-Hubbard model with an effective off-site three-body tunneling on a one-dimensional optical lattice,namely the mean-field method with two-site and the density matrix renormalization group method.In the third chapter,we simulate the anyon Hubbard model on a one-dimensional optical lattice by means of mean-field and density matrix renormalization group methods.We analyze the single particle correlation function,momentum distribution,and find the superfluid phases condensed at a momentum 0<?<? with broken reflectional symmetry,as well as an emergent two component phase PP phase at large fillings ??1.5.In chapter IV,we apply the density matrix renormalization group method to simulate the Bose-Hubbard model with an effective off-site three-body tunneling on a one-dimensional optical lattice.We studies both the hardcore and softcore Bose-Hubbard models,and then finds if the off-site trimer superfluid and partially off-site trimer superfluid phases exist in the softcore Bose-Hubbard model,and the phase diagrams are also discussed.In chapter V,the conclusions are presented.