Eur. Phys. J. B 13, 55-73 (2000)
https://doi.org/10.1007/s100510050010

Magnetic properties of zig-zag ladders ^*

¹ Physikalisches Institut der Universität Bonn, Nußallee 12, 53115 Bonn, Germany
² International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste, Italy
³ Institut für Theoretische Physik, ETH-Hönggerberg, 8093 Zürich, Switzerland
⁴ Laboratoire de Physique (URA 1325 du CNRS associée à l'École Normale Supérieure de Lyon) , Groupe de Physique Théorique, ENS Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France

Corresponding author: ^a a.honecker@tu-bs.de

Received: 11 February 1999
Revised: 16 June 1999
Published online: 15 January 2000

Abstract

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.