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**Authors:**Gregor A. Foltin, __Salvatore R. Manmana,__ Frédéric Mila, and
Kai P. Schmidt

We report our findings for a quasi-2D approximation to the Shastry-Sutherland lattice which we refer to as a 4-leg Shastry-Sutherland tube. This system consists of mutually orthogonal $S=1/2$ Heisenberg dimers which are coupled via an inter-dimer coupling $J'$. Using pCUTs and the DMRG, we identify as a function of $J'$ and the magnetic field a series of magnetization plateaux. Here we focus on the ones at 1/8 and 1/4. In contrast to previous findings for coupled dimer systems, quantum fluctuations induced by correlated hopping terms influence significantly the nature of these Mott insulating states. We characterize the state at 1/4 to be a semi-classical one, and the one at 1/8 to possess a stripe structure caused by an interplay of the peculiar geometry and the inter-dimer couplings. This particular finding suggests the system to be in an insulating state in the longitudinal, but a maximally entangled state in the transverse direction. We discuss possible relations of our findings to the full 2D system, which is the underlying model for the description of the quantum magnetic material SrCu(BO$_3$)$_2$.

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