Entanglement and Emergence in Simulations of Quantum Matter

本世纪将在科学家设计材料、设备和信息系统的方式上发生一场前所未有的革命。这场革命将通过利用量子力学的非凡性质来开启，这将为材料科学和信息技术带来新的可能性。要做到这一点，材料和系统将从原子水平设计到宏观尺度。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，而且很少能通过分析处理得到精确的解。相反，在这个研究计划中，我们将使用最先进的数值工具，通过对单个组成电子、原子和自旋的建模，在其核心模拟新的量子系统。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的或奇异的现象，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，或根本上的新激发，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。除了它们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件。这项研究的一个特别目标将是确定哪些类型的量子现象是“浮现的”，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--这是一项唯一适合通过计算机模拟进行探索的任务。此外，我们将专注于根据纠缠特性对奇异的量子相位和激发进行分类，这是由于最近算法技术的创新使之成为可能。这样，所提出的计算机模拟将为将成为21世纪量子材料基础的量子现象的类型形成坚实的理论基础。

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.