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

In this paper, we propose a method to understand the nature of 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 ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-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 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.