SO( <i>N</i> ) Singlet‐Projection Model on the Pyrochlore Lattice

We present an extensive quantum Monte Carlo (QMC) study of a nearest‐neighbor, singlet‐projection model on the pyrochlore lattice that exhibits SO( N ) symmetry and is sign‐problem‐free. We found that, in contrast to the previously studied two‐dimensional (2D) variations of this model that harbor critical points between their ground state phases, the non‐bipartite pyrochlore lattice in three spatial dimensions appears to exhibit a first‐order transition between a magnetically‐ordered (MO) phase and some, as yet uncharacterized, paramagnetic (PM) phase. We also observe that the MO phase survives to a relatively large value of N = 8 and that it is gone for N = 9.