  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 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 flat band, which is the origin of the rung-pair
localization. We also study the multi-particle dynamics of the Bose-Hubbard
ladder model, which is beyond the singleparticle picture. In this case, we find
that the localization can still survive despite of 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 flat band, which is induced by on-site interaction and
specific lattice symmetry.
