Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo in Atomic and Condensed Matter Physics

合作研究：原子和凝聚态物理中的蠕虫算法和图解蒙特卡罗

• 批准号: 1005543
• 负责人: Boris Svistunov
• 金额: $ 87万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005543&HistoricalAwards=false
• 关键词: Collaborative; Research; Worm; Algorithm; Diagrammatic

This project focuses on ultra-cold atoms and quantum crystals where collective behavior is governed by laws of quantum mechanics. Understanding these systems is crucial for theoretical modeling, condensed matter physics, and materials science because of the prospects for discovering new states of matter. One of such states --- supersolidity of Helium-4 --- remains one of the biggest puzzles in the modern low-temperature physics. One finds interacting quantum systems across all fields of physics, quantum chemistry, and materials science and there is urgent need for universal unbiased first-principles methods to deal with them in their full complexity. This project is aimed at developing such methods, with the particular focus on: (i) Studying collective phenomena in disordered, multi-component, and other non-trivial cold-atomic ensembles in optical lattices and in continuous space, including interacting fermions in the crossover regime with physics intermediate between that of conventional superconductors and bosonic superlfuids; (ii) Understanding the microscopic picture behind and novel phenomena associated with the supersolidity in Helium-4; (iii) Advancing Monte Carlo techniques and algorithms as a universal tool for solving quantum-statistical problems - diagrammatic Monte Carlo for fermions and Worm Algorithm for bosons.An unbiased theoretical description of collective quantum phenomena is of vital interdisciplinary importance for a number of applied and fundamental areas, such as quantum computing and high-energy physics. High-end computing methods and techniques often find applications outside the physics community. Simulations of complex models with multiple constraints, randomness, and a variable number of continuous parameters are typical in polymer science, neural networks, computer science, behavioral, social and economics studies. The algorithms developed in the project provide an example of how some of the difficulties may be circumvented. An integral part of the project is the training of graduate students and post-doctoral associate in advanced numeric techniques, quantum statistics, topical problems of atomic and solid state physics, network administration, and parallel supercomputing. This project includes: (i) developing tools for visualizing quantum statistical phenomena in terms of Feynman's paths (worldlines) and diagrams; (ii) maintaining an interactive web site popularizing, teaching and disseminating new algorithms and codes; (iii) upgrading and administrating major shared computational facilities at both Universities; (iv) developing and teaching a multi-institutional graduate tele-course on advanced numeric methods; (v) writing a book on superfluid states of matter and developing on its basis a graduate course; (vi) promoting higher standards in science education at schools; (vii) organizing a workshop on supersolidity.

该项目的重点是超冷原子和量子晶体，其中集体行为受量子力学定律管辖。了解这些系统对于理论建模，凝结物理学和材料科学至关重要，因为发现了新的物质状态。这样的状态之一 - 氦4 ---超验证性 - - 仍然是现代低温物理学中最大的难题之一。人们发现了各个物理，量子化学和材料科学领域的相互作用量子系统，并且迫切需要普遍无偏见的第一原理方法来应对它们的全部复杂性。该项目旨在开发此类方法，特别关注：（i）在光学晶格和连续空间中研究无序，多组分和其他非客气的冷原子合奏中的集体现象，包括在跨界范围内与传统的超跨副群和bosbosonic sposornics supsposornics supsposorm sposludfuidss中间的跨界效率相互作用； （ii）理解背后的微观图片和与氦4中的超摩托关系相关的新现象； （iii）推进蒙特卡洛技术和算法是解决量子统计问题的通用工具 - 用于玻色子的费米子和蠕虫算法的示意蒙特卡洛。集体量子现象的理论描述无公正的理论描述，具有重要的和量子量的量化和基础计算的重要性，例如重要的跨学科重要性。高端计算方法和技术经常在物理社区之外找到应用。在聚合物科学，神经网络，计算机科学，行为，社会和经济学研究中，具有多个约束，随机性和可变连续参数的复杂模型的模拟是典型的。项目中开发的算法提供了一个例子，说明了如何规避某些困难。该项目不可或缺的一部分是对高级数字技术，量子统计，原子状态和固态物理学，网络管理和平行超级计算的研究生和博士后助理的培训。 该项目包括：（i）开发以Feynman的路径（世界路线）和图表来可视化量子统计现象的工具； （ii）维护交互式网站的普及，教学和传播新算法和代码； （iii）在两所大学中升级和管理主要的共享计算设施； （iv）开发和教授有关高级数字方法的多机构的研究生电视课程； （v）写一本关于物质超流体状态并以研究生课程发展的书； （vi）促进学校科学教育的较高标准； （vii）组织一个关于超词的研讨会。