The S=12 XY and XYZ Models on the Two- or Higher-Dimensional Hypercubic Lattice Do Not Possess Nontrivial Local Conserved Quantities

Abstract

We study the S=12 quantum spin system on the d-dimensional hypercubic lattice with d≥2 with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently developed for quantum spin chains, we prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian. This result strongly suggests that the model is nonintegrable. We note that our result applies to the XX model without a magnetic field, which is one of the easiest solvable models in one dimension.