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.

Part of the computations of this work were performed with the High Capacity Computational Cluster for Physics of UCM (HC3PHYS UCM), funded in part by UCM and in part with FEDER funds. We acknowledge financial support from DGS grants under contracts BFM 2003-05316-C02-01, FIS2006-04885, and the ESF Science Programme INSTANS 2005-2010.

6 pages.-- Revtex4 file, color figures.-- PACS numbers: 75.10.Jm 75.10.-b 74.20.Mn.

Peer reviewed