Staggered ground states in an optical lattice

Nonstandard Bose-Hubbard models can exhibit rich ground-state phase diagrams, even when considering the one-dimensional limit. Using a self-consistent Gutzwiller diagonalization approach, we study the mean-field ground-state properties of a long-range interacting atomic gas in a one-dimensional optical lattice. We first confirm that the inclusion of long-range two-body interactions to the standard Bose-Hubbard model introduces density-wave and supersolid phases. However, the introduction of pair and density-dependent tunneling can result in new phases with two-site periodic density, single-particle transport, and two-body transport order parameters. These staggered phases are potentially a mean-field signature of the known novel twisted superfluids found via a density-matrix renormalization group approach [Phys. Rev. A 94, 011603(R) (2016)2469-992610.1103/PhysRevA.94.011603]. We also observe other unconventional phases which are characterized by sign staggered order parameters between adjacent lattice sites.