Quantum criticality in antiferromagnetic quantum spin ladders with long-range interactions

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 Neel 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.