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

该项目的重点是在光学晶格中冷原子系统的强相关相，其中集体行为由量子力学定律支配。典型的强关联费米子系统--Hubbard模型和BCS-BEC交叉区中的共振费米子--是冷原子研究和凝聚态研究的核心。理解固体4 He中的量子塑性和超输运仍然是现代低温物理的重大挑战之一。在物理学、量子化学和材料科学的所有领域，都迫切需要一种普遍的、无偏的第一原理方法来研究强关联的费米子系统。从头算和模型模拟提供了关于这些系统的定量和定性性质的重要信息，测试分析预测并帮助建立适当的理论框架，为实验数据的明确分析和测量技术的进一步发展奠定基础。具体而言，该项目旨在（i）为连续空间和晶格费米子/费米子化系统开发通用图解蒙特卡罗（DiagMC）工具：共振费米子，Hubbard模型和受抑自旋系统，（ii）了解固体氦-4中的量子塑性和超输运，（iii）对量子临界现象和超冷原子的新相进行蠕虫算法（WA）研究：非限定临界性、普适临界动力学、极性分子多重束缚复合物的相。集体量子现象的无偏理论描述对于一些应用和基础领域（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。

This project focuses on strongly correlated phases of cold-atomic systems in optical lattices where collective behavior is governed by laws of quantum mechanics. The prototypical strongly correlated fermionic systems -- the Hubbard model and resonant fermions in the regime of BCS-BEC crossover -- are central in the fields of the cold atom research and condensed matter. Understanding quantum plasticity and super transport in solid 4He remains one of big challenges in modern low-temperature physics. There is urgent need for universal unbiased first-principles methods for strongly correlated fermionic systems across all fields of physics, quantum chemistry, and materials science. Ab initio and model simulations provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions and help establish the proper theoretical framework, lay the ground for the unambiguous analysis of experimental data and further development of measuring techniques. In particular, this project aims to (i) develop generic diagrammatic Monte Carlo (DiagMC) tools for continuous-space and lattice fermionic/fermionized systems: resonant fermions, Hubbard model, and frustrated spin systems, (ii) understand quantum plasticity and supertransport in solid helium-4, (iii) perform Worm Algorithm (WA) studies of quantum-critical phenomena and novel phases of ultra-cold atoms: deconfined criticality, universal critical dynamics, phases of multi-bound complexes of polar molecules.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.