L. Li

Topological phases of generalized Su-Schrieffer-Heeger models

We study the extended Su-Schrieffer-Heeger model with both nearest-neighbor and next-nearest-neighbor hopping strengths cyclically modulated and find the family of the model system exhibiting topologically nontrivial phases, which can be characterized by a nonzero Chern number defined in a two-dimensional space spanned by the momentum and a modulation parameter. It is interesting that the model has a similar phase diagram to that of the well-known Haldane model. We propose to use photonic crystal systems as the ideal systems to fabricate our model systems and probe their topological properties. Some other models with modulated on-site potentials are also found to exhibit similar phase diagrams, and their connection to the Haldane model is revealed.

Fractional Topological States of Dipolar Fermions in One-Dimensional Optical Superlattices

We study the properties of dipolar fermions trapped in one-dimensional bichromatic optical lattices and show the existence of fractional topological states in the presence of strong dipole-dipole interactions. We find some interesting connections between fractional topological states in one-dimensional superlattices and the fractional quantum Hall states: (i)xa0the one-dimensional fractional topological states for systems at filling factor ν=1/p have p-fold degeneracy, (ii)xa0the quasihole excitations fulfill the same counting rule as that of fractional quantum Hall states, and (iii)xa0the total Chern number of p-fold degenerate states is a nonzero integer. The existence of crystalline order in our system is also consistent with the thin-torus limit of the fractional quantum Hall state on a torus. The possible experimental realization in cold atomic systems offers a new platform for the study of fractional topological phases in one-dimensional superlattice systems.

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions.

The ground state properties of the Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interactions are investigated by means of the exact diagonalization method. We show that the appearance of N-crests in the density profile of a trapped N-fermion system is a natural result of fermionization between antiparallel-spin fermions in the strongly repulsive limit and cannot be taken as the only signature of the Wigner crystal phase, as the static structure factor does not show any signature of crystallization. In contrast, both the density distribution and the static structure factor of the Hubbard model with strong long-range interactions display clear signatures of the Wigner crystal phase. Our results indicate the important role of long-range interaction in the formation of the Wigner crystal phase.