Simulation Studies of Ground State Phases and Criticality in Correlated Quantum Matter

技术说明：该奖项支持旨在阐明强关联电子系统中复杂基态和量子相变的本质的计算和理论研究。研究涉及对量子自旋模型的大规模模拟研究。这些方法将使用先进的量子蒙特卡罗方法，主要是那些基于PI开发的量子统计力学的随机级数展开(SSE)公式的方法。PI将继续开发模拟算法。要研究的具体模型包括带有环交换项的二维硬核玻色子模型。这项工作的一个目的是准确地描述超流到价键-固体的转变，这被认为是一个“去受限”的量子临界点。我们将研究海森堡模型，以实现O(3)对称的反铁磁到自旋-液体的相变。我们将研究具有稀释形式的强无序的海森堡模型，目的是描述在这个框架内可能发生的量子相变。这项工作将产生新的SSE算法，可能会对其他领域的研究产生影响，例如格子规范理论和量子信息理论。除了在物理学和高级科学计算方面培训学生外，该奖项还支持一个网站的建设，在该网站中，SSE方法以教学方式展示，并与各种模型的范例程序一起。非技术性解释：该奖项支持计算和理论研究，这些研究涉及现代理论凝聚态物理学的核心问题，这些问题受到材料的发现的启发，在材料中，电子自我组织形成不寻常的物质状态。高温超导体和相关化合物就是这些材料之一。PI将使用先进的计算方法和简化的模型，旨在剔除不必要的细节，并专注于理解这些复杂材料所需的基本物理。旨在确定这些模型的精确解的计算技术的使用补充了分析理论的努力，并提供了传统实验无法获得的洞察力。PI将进一步研究在绝对零度下发生的电子相之间的转变，这超出了相变的标准理论。这种新的相变促进了我们对相变的理解，并可能成为理解高温超导体和其他强关联材料这一具有挑战性的难题的关键部分。对这种和其他量子相变的理解可能会对物理学和其他领域产生影响。该提案还支持一项外联活动，使国际和平研究所的计算方法更广泛地为研究界所用。

TECHNICAL EXPLANATION:This award supports computational and theoretical research that aims to elucidate the nature of complex ground states and quantum phase transitions in strongly correlated electron systems. Research involves large-scale simulation studies of quantum spin models. These will use advanced quantum Monte Carlo methods, primarily those based on the stochastic series expansion (SSE) formulation of quantum statistical mechanics developed by the PI. The PI will continue to develop simulation algorithms. The specific models to be studied include a two-dimensional hard-core boson model with a ring-exchange term. An aim of this work is to accurately characterize the superfluid to valence-bond-solid transition, which has been proposed to be a "deconfined" quantum-critical point. A Heisenberg model will be studied with the aim of achieving an O(3)-symmetric antiferromagnetic to spin-liquid transition. Heisenberg models with strong disorder in the form of dilution will be investigated with the aim of characterizing the quantum phase transitions that are possible within this framework. New SSE algorithms that will result from this work may impact research in other fields, for example lattice gauge theory and quantum information theory. Beyond training students in physics and advanced scientific computing, this award supports the construction of a web-site in which the SSE method is presented in a pedagogical manner and along with example programs for a various models.NON-TECHNICAL EXPLANATION:This award supports computational and theoretical research that engages issues at the heart of modern theoretical condensed matter physics that are inspired by the discovery of materials in which the electrons organize themselves to form unusual states of matter. High temperature superconductors and related compounds are among these materials. The PI will use advanced computational methods and streamlined models designed to strip away unnecessary detail and focus on the essential physics needed to understand these complex materials. The use of computational techniques aimed at ascertaining the exact solution to these models complements analytical theory efforts and provides insight that is not accessible to traditional experiments. The PI will further investigate a transformation among electronic phases that occurs at the absolute zero of temperature, and lies outside the standard theory of phase transitions. This new kind of phase transition advances our understanding of phase transitions and may be a key piece in the challenging puzzle of understanding high temperature superconductors and other strongly correlated materials. The understanding of this and other quantum phase transitions may have impact across physics and other fields. The proposal also supports an outreach activity to make the PI's computational methods more broadly accessible to the research community.