Magnetization plateaux inN-leg spin ladders

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single $\mathrm{XXZ}$ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of $N$ weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number $N$ of cylindrically coupled chains numerically. For $N=3\mathrm{}$ we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\overrightarrow{N}\infty$.