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

这个项目集中在光学晶格中冷原子系统的强关联相，其中集体行为受量子力学定律的支配。典型的强关联费米子系统--Hubbard模型和BCS-BEC交叉区域的共振费米子--是冷原子研究和凝聚态物质领域的中心。理解固体4He的量子可塑性和超输运仍然是现代低温物理学中的一大挑战。对于物理、量子化学和材料科学的所有领域的强关联费米子系统，迫切需要通用的无偏第一原理方法。从头算和模型模拟提供了有关这些系统的定量和定性性质的关键信息，检验了分析预测，并有助于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了基础。特别是，这个项目的目标是(I)开发用于连续空间和晶格费米子/费米化系统：共振费米子、Hubbard模型和受阻自旋系统的通用图解蒙特卡罗(DiagMC)工具，(Ii)了解固体氦-4中的量子可塑性和超输运，(Iii)执行Worm算法(WA)研究量子临界现象和超冷原子的新相：去受限临界、普适临界动力学、极性分子的多束缚络合物的相。集体量子现象的无偏见的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，具有至关重要的交叉学科意义。高端计算方法和技术经常在物理界之外得到应用。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，对具有多个约束、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对研究生和博士后进行高级数字技术、量子统计、原子和固态物理的主题问题、网络管理和并行超级计算方面的培训。

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.