Localization of rung pairs in a hard-core Bose-Hubbard ladder

Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using the center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sublattice symmetry. Under the condition of the hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flatband, which is the origin of the rung-pair localization. We also study the multiparticle dynamics of the Bose-Hubbard ladder model, which is beyond the single-particle picture. In this case, we find that the localization can still survive despite the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flatband, which is induced by on-site interaction and specific lattice symmetry.