Extended Study Of Ground State Properties In SSH Model

Ultracold atomic systems have the advantage of being clean and controllable,providing an ideal platform for studying strongly correlated topological insulators.The SSH(Su-Schrieffer-Heeger)model has been experimentally implemented in the ultracold atoms of a one-dimensional(1D)dimerized optical superlattice,which is one of the most basic systems of topological insulators.A topological insulator is a hot research problem in condensed matter physics in recent years,and the band structure in the body is the same as that of the insulator,and there is always a gapless edge state on the surface,which provides great application value for semiconductor devices and other fields.Various extensions have been made to the SSH model from a theoretical point of view,such as the SSH model considering the sub-nearest transition,the non-Ermi SSH model,and the Spin-Orbit Coupling(SOC)SSH model,which exhibit richer and more diverse topological properties than the SSH model.In fermi subsystems,SOC plays an important role in many topological non-trivial phases.A pair of tunable Raman lasers are used to realize modularly SOC in ultracold fermion systems,and this artificially modulated SOC changes the single-particle dispersion relationship,which in turn profoundly affects the physical properties of the system.Based on the above background,we use the Matrix Product State(MPS)method to study the ground state properties of the extended SSH model,calculate the entanglement entropy,entanglement spectrum,static structural factor,density distribution,order parameter,and other related parameters,and the research results are as follows:(1)The density structural factor peak will undergo step behavior at the phase transition point of the SSH model,and under small size,the structural factor peak will suddenly change at the phase transition point,and when the system size is large enough,the mutation disappears,and the peak value shows singularity.When SOC and Repulsive Particle Interaction(RPI)are introduced into the system,the behavior of the density structural factor peak at the phase transition point changes.When SOC acts alone,the density structural factor at the phase change point becomes step-by-step,and with the repulsion action alone,the peak value of the density structural factor appears obvious singularity at the phase transition point,and when the two act together,the peak of the density structural factor does not behave strangely at the phase transition point.(2)In the extended SSH model with SOC and RPI,there are different numbers of non-trivial topology edge states or mediocre states in the system under different parameters.In the interval with large SOC intensity,the strong rejection causes the chiral symmetry of the ground state of the system to spontaneously break,and the competition between the two produces a new topological trivial phase density wave phase(DW).The particle number density distribution of the DW phase showed uniform oscillation,and the particle number density distribution of spin up and down also showed uniform oscillation and completely coincided.Furthermore,we study the influence of the Zeeman field on the DW phase,and the system transitions from the DW phase to the mediocre phase during the gradual increase of Zeeman field strength.Another extension of the SSH model is the SSH4 model,which introduces Zeeman fields,SOC,and other parameters to make its physical image more complex.The next step in the study of the ground state properties and topological properties of the SSH4 model will provide a way to simulate fermion topological phases using cold atoms in the optical lattice.