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

这个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的支配。了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。其中一种状态——氦-4的超固态——仍然是现代低温物理学中最大的难题之一。人们发现相互作用的量子系统跨越物理学、量子化学和材料科学的所有领域，迫切需要普遍的无偏第一原理方法来处理它们的全部复杂性。本项目旨在发展这样的方法，特别关注：(1)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，包括介于传统超导体和玻色子超流体之间的交叉态中的相互作用费米子；（ii）了解氦-4超固体背后的微观图景和与之相关的新现象；（iii）推进蒙特卡罗技术和算法作为解决量子统计问题的通用工具-费米子图解蒙特卡罗和玻色子蠕虫算法。对集体量子现象进行公正的理论描述对于量子计算和高能物理等许多应用和基础领域具有至关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，具有多重约束、随机性和可变数量连续参数的复杂模型的仿真是典型的。该项目中开发的算法提供了一个如何绕过一些困难的例子。该项目的一个组成部分是在高级数值技术、量子统计、原子和固体物理的专题问题、网络管理和并行超级计算方面培养研究生和博士后。该项目包括：(i)开发工具，用于根据费曼路径（世界线）和图表可视化量子统计现象；（ii）维持一个互动网站，普及、教授和传播新的算法和代码；（iii）提升及管理两所大学共用的主要电脑设施；（iv）开发和教授多机构研究生远程高级数值方法课程；(v)撰写一本关于物质超流体状态的书，并在其基础上发展一门研究生课程；（六）提高学校的科学教育水平；组织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.