  We study a generalized quantum spin ladder with staggered long range
interactions that decay as a power-law with exponent $\alpha$. Using the
density matrix renormalization group (DMRG) method and exact diagonalization,
we show that this model undergoes a transition from a rung-dimer phase
characterized by a non-local string order parameter, to a symmetry broken
N\'eel phase at $\alpha_c\sim 2.1$. We find evidence that the transition is
second order with a dynamic critical exponent $z=1$ and $\nu\approx 1.2$. In
the magnetically ordered phase, the spectrum exhibits gapless modes, while
excitations in the gapped phase are well described in terms of triplons --
bound states of spinons across the legs. We obtained the momentum resolved spin
dynamic structure factor numerically and found that the triplon band is well
defined at high energies and adiabatically connected to the magnon dispersion.
However, at low energies it emerges as the lower edge of continuum of
excitations that shifts to high energies across the transition. We further
discuss the possibility of deconfined criticality in this model.
