Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction

TL;DR

This paper generalizes the Majumdar-Ghosh model to arbitrary spin-$S$ chains with complex interactions, rigorously proving the existence of exact dimerized ground states and analyzing phase diagrams using theoretical and numerical methods.

Contribution

It introduces a rigorous proof of exact dimerized ground states in generalized spin-$S$ chains and explores their phase diagrams with effective field theories and numerical analysis.

Findings

Existence of exact dimerized ground states in parameter regions.

Universality classes of phase transitions identified by level-$2S$ SU(2) WZW and Gaussian models.

Phase diagrams for $S=1$ and $S=3/2$ systems determined through exact diagonalization.

Abstract

We discuss spin-$S$ antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary $S$. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-$2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of $S=1$ and $S=3/2$ systems by using exact diagonalization and level spectroscopy.