Massive and Massless Behavior in Dimerized Spin Ladders

We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lanczos diagonalization techniques. Although both interchain ( $J^{\prime }$) and dimerization ( $\delta$) couplings favor a gapful phase, it is shown that a suitable choice of these interactions yields massless spin excitations. We also discuss the influence of different arrays of relative dimerization on the appearance of nontrivial magnetization plateaus.