Commensurate supersolids and re-entrant transitions in an extended Bose-Hubbard ladder

We investigate the ground state phases of an extended Bose-Hubbard ladder of unit filling via the density-matrix-renormalization-group method and, in particular, the effect of rung-hoppings. In contrast to a single-chain, a commensurate supersolid emerges, and based on the Luttinger parameter, we classify them into two types. The latter leads to a reentrant gapless behavior as the onsite interaction is increased while keeping all other parameters intact. A reentrant gapped transition is also found as a function of nearest-neighbor interactions. Further, we show that the string order characterizing the Haldane phase vanishes for a finite inter-chain hopping amplitude, however small it is. Finally, we propose two experimental platforms to observe our findings, using either dipolar atoms or polar molecules and Rydberg admixed atoms.