Quantum Monte Carlo Simulation of an SO(N) Singlet Projector Model on the Pyrochlore Lattice*

Over the last decade, the search for deconfined quantum critical points on a variety of models and lattices has produced many concrete numerical examples and revealed opportunities for finding exotic quantum phases, such as spin liquids. Having studied all two-dimensional lattices of interest, our goal was to expand our computational method’s functionality to be able to handle a three-dimensional lattice, namely the Pyrochlore lattice (Fd3m). On this lattice, we deployed an SO(N)-symmetric singlet-projector model using a stochastic series expansion quantum Monte Carlo simulation (the “computational method”). We used this method to gather evidence for the existence of a magnetically (quadrupolar) ordered phase of Pyrochlore up to N=N1, beyond which we expect that no such phase can occur. We discuss what is known about the phase of Pyrochlore when N>>N1, and the particularities of the transition to this phase, from the magnetically ordered (N<N1) phase. Finally, we discuss our plans for the project going forward.