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

Quantum simulation experimentally 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, the rung-pair localization can exist both at the edges and in the bulk. Using center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sub-lattice symmetry. Under the condition of hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy mode, which is the origin of the rung-pair localization. In addition, we also study the dynamics of the Bose-Hubbard ladder model with multiple rung pairs. Using time evolving block decimation method, we demonstrate that the system can display a localization similar to the many-body localization. The entanglement entropies exhibit a long-time logarithmic growth, and the corresponding saturated values satisfy a volume law.