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

相关量子物质的基态相和临界性的模拟研究

• 批准号: 0803510
• 负责人: Anders Sandvik
• 金额: $ 36万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0803510&HistoricalAwards=false
• 关键词: Simulation; Studies; Ground; State; Phases

TECHNICAL SUMMARY:This award supports theoretical research and education in computer simulation studies of ground state phases and criticality in correlated quantum matter. Large-scale computer simulations of lattice quantum many-body systems are carried out in this work. These studies are inspired by the phenomenology of strongly-correlated electron systems?their complex phase diagrams and quantum phase transitions in particular?but are not complete descriptions of specific materials (because of the computational complexity). Instead, simplified quantum spin models are used to capture physical phenomena of interest and gain generically valid insights through unbiased simulations. Complex ground states and phase transitions induced by competing interactions are studied, focusing in particular on the transition between an antiferromagnetic (AF) and a valence-bond-solid in two-dimensional quantum spin systems. The transition and the VBS phase are investigated using sophisticated numerical methods. Research into novel computational algorithms based on states defined by tensor-networks and related objects are also carried out. Such methods have the potential to enable studies of ground states of previously intractable frustrated quantum spin systems.The effort undertaken has broader impacts with both scientific and educational consequences. The work on numerical simulation techniques produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on tensor-network and related states for describing correlated quantum states is also of interest in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with example programs for a variety of models.NONTECHNICAL SUMMARY:This award supports theoretical research and education in the use of state-of-the-art computer simulation studies of novel electronic structures that have been discovered in exotic materials like the two-dimensional carbon sheets called graphene. Large-scale computer simulations of quantum physics that describes these systems are carried out in this work. These studies are inspired by experiments and discovery of these novel materials, but are not aimed at complete descriptions of specific materials because such detailed numerical studies are not yet possible because of the computational complexity. Instead, simplified quantum spin models are used in order to capture physical phenomena of interest, with the objective of gaining new generically valid insights through unbiased computer simulations. The effort undertaken has broader impacts with both scientific and educational consequences. The work on computer simulations produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on novel computational algorithms is also important in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with easy-to-use example programs for a variety of models.

技术概述：该奖项支持相关量子物质中基态相和临界性的计算机模拟研究的理论研究和教育。本文对晶格量子多体系统进行了大规模的计算机模拟。这些研究的灵感来自于强关联电子系统的现象学--特别是它们的复杂相图和量子相变--但并不是对特定材料的完整描述(因为计算复杂)。相反，简化的量子自旋模型被用来捕捉感兴趣的物理现象，并通过无偏见的模拟获得普遍有效的见解。研究了由竞争相互作用引起的复杂基态和相变，特别是二维量子自旋系统中反铁磁(AF)和价键固体之间的相变。用复杂的数值方法研究了相变和VBS相。还研究了基于张量网络定义的状态和相关对象的新型计算算法。这样的方法有可能研究之前难以解决的受挫量子自旋系统的基态。所做的努力具有更广泛的影响，既有科学上的影响，也有教育上的影响。数值模拟技术的工作产生了在凝聚态物理和原子分子物理(超冷凝聚体)中有广泛应用的新算法。研究张量网络和相关态来描述关联量子态的工作也是量子信息论的研究热点。这项建议的一个教育方面，除了对学生进行重要的物理和高级科学计算培训外，还包括一个网站，其中以教学方式介绍了PI开发的各种计算方法，以及各种模型的示例程序。非技术摘要：该奖项支持理论研究和教育，使用最先进的计算机模拟研究，研究在奇异材料中发现的新颖电子结构，如被称为石墨烯的二维碳片。这项工作对描述这些系统的量子物理进行了大规模的计算机模拟。这些研究的灵感来自于这些新材料的实验和发现，但并不是针对特定材料的完整描述，因为由于计算的复杂性，目前还不可能进行这样详细的数值研究。相反，简化的量子自旋模型被用来捕捉感兴趣的物理现象，目的是通过无偏见的计算机模拟获得新的普遍有效的见解。所做的努力产生了更广泛的影响，对科学和教育都产生了影响。计算机模拟的工作产生了新的算法，在凝聚态物理和原子分子物理(超冷凝聚体)中有广泛的应用。新的计算算法的工作在量子信息理论中也是重要的。除了对学生进行重要的物理和高级科学计算培训外，这项建议的一个教育方面是一个网站，其中以教学方式介绍了由国际和平研究所开发的各种计算方法，以及各种模型的易于使用的示例程序。