Two-dimensional spin-1 frustrated Heisenberg model with valence-bond ground states

TL;DR

This paper introduces a novel approach to understanding the quantum disordered phase of a 2D spin-1 frustrated Heisenberg model, revealing doubly degenerate valence-bond solid ground states with nonzero string order.

Contribution

It proposes a new method inspired by fractional quantum Hall effect to exactly identify the ground states of a 2D spin-1 frustrated system, linking quantum Hall physics with frustrated magnetism.

Findings

Ground states are doubly degenerate valence bond solid states.

Ground states exhibit nonzero string order.

Method connects fractional quantum Hall effect with 2D frustrated magnetism.

Abstract

In this paper, we propose a method to understand the nature for the quantum disorder phase of the two-dimensional (2D) high spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose groundstate can be found exactly. By analogy to the pseudo-potential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valance bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used is novel for a 2D spin system and reveals the connection between the fractional quantum hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system, and can be verified by a numerical method.