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

该项目的重点是超冷原子和量子晶体，其中集体行为由量子力学定律支配。理解这些系统对于理论建模、凝聚态物理和材料科学至关重要，因为它们有可能发现新的物质状态。氦-4的超固态是现代低温物理学中最大的难题之一。人们在物理学、量子化学和材料科学的所有领域都发现了相互作用的量子系统，迫切需要通用的无偏第一原理方法来处理它们的全部复杂性。（一）研究光学晶格和连续空间中无序、多组分和其他非平凡冷原子系综中的集体现象，包括交叉区域中的相互作用费米子，其物理学介于常规超导体和玻色子超流体之间; ㈡了解氦-4超固态背后的微观图像和与之相关的新现象;（iii）推动蒙特卡罗技术和算法成为解决量子统计问题的通用工具-费米子的图解Monte Carlo和玻色子的Worm算法。集体量子现象的无偏理论描述对于许多应用和基础领域（如量子计算和高能物理）具有至关重要的跨学科重要性。高端计算方法和技术通常在物理界之外找到应用。具有多个约束、随机性和可变数量的连续参数的复杂模型的模拟在聚合物科学、神经网络、计算机科学、行为、社会和经济学研究中是典型的。该项目中开发的算法提供了一个如何规避某些困难的例子。该项目的一个组成部分是在先进的数值技术，量子统计，原子和固态物理，网络管理和并行超级计算的热点问题的研究生和博士后助理的培训。 该项目包括：（i）开发工具，以费曼路径的形式可视化量子统计现象（ii）维持一个互动网站，推广、教授和传播新的算法和代码;（iii）更新和管理两所大学的主要共用计算设施;（iv）发展和教授一个多机构研究生先进数值方法的远程课程;（v）撰写一本关于超流体物质状态的书，并在此基础上发展一门研究生课程;（vi）提高学校科学教育的水平;（vii）举办一个关于超固体的讲习班。

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.