Twisted Order Parameter applied to Dimerized Ladders

We apply the twisted order parameter (TOP) for dimerized quantum spin ladders to locate the critical phases that separate gapped phases representing quantum spin liquids of various types. Using the DMRG, method we find that the TOP is a good order parameter for these systems regardless the number of legs. As a check, we reproduce with DMRG and periodic boundary conditions the computations previously done with Quantum Montecarlo for one-dimensional S=1/2, S=1, S=3/2 and S=2 Heisenberg chains with alternating bonds.