Dimerized ground states in spin-S frustrated systems

TL;DR

This paper investigates a family of frustrated anti-ferromagnetic spin-$S$ systems with exactly dimerized ground states, analyzing their robustness, phase diagram, and relevance to experimental compounds.

Contribution

It introduces a class of models with exact dimerized ground states, explores their stability under perturbations, and connects theoretical results to experimental spin tube systems.

Findings

Ground states are exactly dimerized without three-body interactions.

Dimerized ground states are robust against weak disorder and perturbations.

Identifies parameter regions where dimerization occurs in related experimental models.

Abstract

We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a fully dimerized ground state. This state can be exactly obtained without the need to include any additional three-body interaction in the model. The simplest members of the family can be used as a building block to generate more complex geometries like spin tubes with a fully dimerized ground state. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as the model for the description of the compound Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space where this model presents dimerization in its ground state.