Dualities and Ground State Phase Diagrams for Quantum Spin-s XYZ Models

Dualities and ground state phase diagrams are discussed for quantum XYZ chains with arbitrary spin s. It is shown that dualities reproduce the ground state phase diagrams for quantum half-integer spin XYZ chains, such as spin s=1/2, 3/2, but not for quantum integer spin XYZ chains, such as spin s=1, 2, in which the so-called symmetry protected topological phase--Haldane phase occurs. Dualities discussed for the one-dimensional quantum XYZ chains with aritrary spin s may be extended to quantum XYZ models with arbitrary spin s on a bipartite lattice in any spatial dimensions, such as square and honeycomb lattices.