Magnetization Plateaux in N-Leg Spin Ladders

TL;DR

This paper investigates magnetization plateaux in N-leg spin ladders using bosonization, strong-coupling expansions, and numerical methods, revealing phase transition universality classes and the persistence of spin gaps.

Contribution

It extends the analysis of magnetization plateaux in spin ladders by combining bosonization, strong-coupling, and numerical approaches, providing new insights into phase transitions and spin gaps.

Findings

Predicted universality classes of phase transitions at plateaux boundaries.

Derived a quantization condition for magnetization values on plateaux.

Numerically observed a spin gap for N=3 that likely persists as N approaches infinity.

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.