Entanglement and Emergence in Simulations of Quantum Matter

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This century will see an unprecedented revolution in the way scientists design materials, devices, and information systems. This revolution will be ushered in by harnessing the extraordinary properties of quantum mechanics, which will allow new possibilities in materials science and information technology. For this to happen, materials and systems will be designed from the atomic level up to the macroscopic scale. However, this presents challenges, since the quantum mechanical equations that govern even the simplest many-body behaviour are vastly complex, and rarely amenable to exact solution by analytical treatments. Instead, in this research program, we will use state-of-the-art numerical tools to simulate novel quantum systems at their very core, by modeling the individual constituent electrons, atoms, and spins. The focus of the research will be on discovering, classifying, and characterizing novel or exotic phenomena that can emerge in quantum many-body systems, such as electronic matter, magnetic materials, or cold atom systems. This phenomena might include new phases of matter, such as spin liquid or topological phases, or fundamentally new excitations, such as fractional charges, spin-charge separated electrons, or particles with anyonic statistics. Beyond their potential to provide innovative materials properties, such phenomena may be suited to construct the fundamental building blocks of future generations of "topological" quantum computers. A particular goal of the research will be to determine which types of quantum phenomea are "emergent", meaning that they can not be derived from the microscopic equations governing the constituent particles - a task uniquely suited for exploration by computer simulations. In addition, we will focus on classifying exotic quantum phases and excitations by their entanglement properties, something made possible by recent innovations in algorithm technology. In this way, the proposed computer simulations will form a firm theoretical basis for the types of quantum phenomena that will be the foundation of 21st century quantum materials.