Phase Exploration in a SU(N)-Symmetric Singlet-Projector Model on the Diamond Lattice Using Quantum Monte Carlo.

We search for exotic quantum phases, such as a spin-liquid phase, and phase transitions that break the traditional Landau-Ginzburg-Wilson (LGW) paradigm, i.e., deconfined quantum criticality, on a simple, local quantum magnetic model; specifically, the SU(N)-symmetric singlet-projector model, which exhibits magnetic order for small N. This model has no sign problem and is therefore easily studied using an exact quantum Monte Carlo algorithm known as the stochastic series expansion. Previous studies have already explored 2D square, honeycomb, triangular, kagome, and 3D pyrochlore lattices; the objective of this project is to consider the 3D diamond lattice to expand our search for exotic behavior. We intend to present evidence of the critical value of N beyond which magnetic order breaks down and then, with the help of additional interaction terms that allow us to tune to the transition point, a determination of the nature of the transition: first-order or continuous. This research was supported by the SURE (Summer Undergraduate Research Experience) award granted by the College of Natural Sciences & Mathematics at Sacramento State and an allocation of supercomputing time through XSEDE (DMR130040) on the Expanse cluster at the San Diego Supercomputing Center.