Critical lines and massive phases in quantum spin ladders with dimerization

Abstract

We determine the existence of critical lines in dimerized quantum spin ladders in their phase diagram of coupling constants using the finite-size density matrix renormalization group algorithm. We consider both staggered and columnar dimerization patterns, and antiferromagnetic and ferromagnetic interleg couplings. The existence of critical phases depends on the precise combination of these patterns. The nature of the massive phases separating the critical lines are characterized with generalized string order parameters that determine their valence-bond-solid content.