Abstract
Until now, our Quantum Monte Carlo simulation could only be applied to several lattices in two dimensions. During this project, I adapted our program to be compatible with the three-dimensional Pyrochlore lattice. Due to the Pyrochlore lattice’s geometrical frustration, the system of quantum ‘nearest neighbor’ spin-spin interactions on the lattice are implicated as a possible source, under certain conditions, of transitions into so-called “exotic” phases of matter, such as quantum spin liquids and valence bond solids. To make our program compatible with Pyrochlore, I was tasked with constructing a model-compatible representation for the lattice, which both satisfied the appropriate periodic boundary conditions, as well as maintained its particular symmetry properties. Furthermore, to fully implement our new lattice, the program’s functionality needed to be expanded to allow measurement and sampling along a third spatial dimension.