Magnetization Plateaux in N-Leg Spin Ladders

Abstract

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 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 we explicitly observe a spin-gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit N to infinity.

31 pages REVTeX, several PostScript figures included using psfig.sty; WWW access to computation of radius of compactification via http://www.he.sissa.it/~honecker/roc.html (backup at http://thew02.physik.uni-bonn.de/~honecker/roc.html); many small changes (concentrated in section II); this is the final version to appear in Phys. Rev. B