Entanglement and Emergence in Simulations of Quantum Matter

在这个世纪，科学家设计材料、设备和信息系统的方式将发生前所未有的革命。 这场革命将通过利用量子力学的非凡特性来实现，这将为材料科学和信息技术提供新的可能性。 为了实现这一点，材料和系统将从原子水平到宏观尺度进行设计。 然而，这带来了挑战，因为即使是最简单的多体行为的量子力学方程也非常复杂，很少能通过分析处理得到精确的解。 相反，在这个研究项目中，我们将使用最先进的数值工具来模拟新的量子系统的核心，通过建模单个组成电子，原子和自旋。 研究的重点将是发现，分类和表征量子多体系统中可能出现的新颖或奇异现象，如电子物质，磁性材料或冷原子系统。 这种现象可能包括物质的新相，如自旋液体或拓扑相，或从根本上新的激发，如分数电荷，自旋电荷分离的电子，或具有任意子统计的粒子。 除了提供创新材料特性的潜力之外，这种现象可能适合于构建未来几代“拓扑”量子计算机的基本构建模块。 这项研究的一个特别目标是确定哪些类型的量子现象是“涌现的”，这意味着它们不能从控制组成粒子的微观方程中推导出来-这是一项非常适合通过计算机模拟进行探索的任务。 此外，我们将专注于分类奇异量子相位和激发他们的纠缠特性，最近的算法技术的创新成为可能。 通过这种方式，计算机模拟将为量子现象的类型奠定坚实的理论基础，而量子现象的类型将成为21世纪世纪量子材料的基础。

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.