Magnetic Properties of Zig-Zag Ladders

TL;DR

This paper investigates the magnetic phase diagram of zig-zag spin-1/2 Heisenberg ladders, revealing how various couplings and external fields induce spin gaps and magnetization plateaux through analytical and numerical methods.

Contribution

It provides a combined analytical and numerical analysis of how different couplings and external influences create spin gaps and magnetization plateaux in zig-zag ladders.

Findings

Spin gaps and magnetization plateaux depend on coupling types and external fields.

Unusual behavior observed in ferromagnetically coupled antiferromagnetic chains.

Three-leg ladders can exhibit spin gaps and non-trivial magnetization plateaux.

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.