We propose to carry out large-scale computer simulations to explore the properties of emergence in lattice models of quantum matter. In particular, we are interested in searching for exotic quantum phenomena that emerge from realistic microscopic models related to materials at low temperatures. These phenomena will primarily include exotic quantum quasiparticles, which may contain fractional charges, spin-charge separated degrees of freedom, or anyonic statistics; and which display some form of long-range entanglement, both in gapped systems (e.g. topological order) and gapless systems (e.g. exotic quantum criticality). The use of advanced computer simulations will allow us to establish cases where emergent phenomena arises from specific microscopic many-body models, by solving the models directly. We therefore expect that one outcome will be a definitive determination of which specific types of emergent phenomena are strongly emergent, and which are weakly emergent. In addition, we plan to classify emergent entities based on their entanglement properties. In general, we hope to use these studies as part of a broader strategy to examine how entanglement patterns act as an organizing principle for different emergent quantum phenomena. This work will exploit the unique abilities of the Project Leaders, utilizing a combination of novel numerical algorithms for quantum lattice models, and high-performance computational resources. Together, Melko and Vidal will train and employ Project Personnel using Quantum Monte Carlo and Tensor Network techniques, to look at physically-relevant models of interacting quantum spins, bosons, and fermions. We are confident that this unique computer simulation approach will yield an enduring understanding of the role that strong emergence plays in real quantum materials and matter. It also has a high potential for delivering disruptive innovation to our current paradigm of the organizing principles of matter in the universe.