Magnetization Plateaus in Spin Chains: “Haldane Gap” for Half-Integer Spins

TLDR

Zero‑temperature quantum spin chains with axial symmetry are considered in a uniform magnetic field. The study investigates the topological quantization of magnetization plateaus in integer and half‑integer spin chains and the conditions for their occurrence. The authors analyze several S = 3/2, m = 1/2 spin‑chain models to identify two distinct massive phases at the plateau. They find two massive phases at the S = 3/2, m = 1/2 plateau, one of which is a Haldane‑gap phase for half‑integer spin.

Abstract

We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, $S$, the magnetization curve can have plateaus and we argue that the magnetization per site $m$ is topologically quantized as $q (S - m)= integer$ at the plateaus, where $q$ is the period of the groundstate. We also discuss conditions for the presence of the plateau at those quantized values. For $S=3/2$ and $m=1/2$, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer $S$.