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We study the topological properties of hardcore bosons on a two-leg ladderconsisting of two Su-Schrieffer-Heeger (SSH) chains that are coupled viahopping and interaction. We chart out the phase diagram for the system and showthat based on the relative hopping dimerization pattern along the legs,distinctly different topological phases and phase transitions can occur. Whenthe dimerization along the legs are uniform, we find that the topologicalnature vanishes for even the slightest rung hopping. For staggereddimerization, the system exhibits a well defined topological character and atopological phase transition as a function of rung hopping. While thetopological phase shows bond order character, the trivial phase shows thebehavior of a rung-Mott insulator. For this case, the topological nature isfound to survive even in the presence of finite inter-leg interactions.Moreover, we find that the critical point of the topological phase transitionshifts to a higher or a lower rung hopping strength depending on the attractiveor repulsive nature of the interaction. To highlight the marked effects ofinteractions, we propose a scheme involving a Thouless charge pump thatprovides insights for the topological phases characterized by a quantisedparticle transport through a periodic modulation of appropriate systemparameters. In our studies, we show an interaction induced charge pumpingfollowing specific pumping protocols in the case of staggered dimerization.

Interacting bosons on a Su-Schrieffer-Heeger ladder: Topological phases and Thouless pumping