Multi-Worm Algorithm for Path Integral Quantum Monte Carlo in Ultracold Dipolar Gases

超冷偶极气体中路径积分量子蒙特卡罗的多蠕虫算法

• 批准号: 1552978
• 负责人: Barbara Capogrosso-Sansone
• 金额: $ 27.6万
• 依托单位: Clark University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-30 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1552978&HistoricalAwards=false
• 关键词: Multi; Worm; Algorithm; Path; Integral

The goal of this project is to investigate quantum phases of strongly correlated systems with an emphasis on cold polar molecule setups. Strong correlations are at the core of many fascinating biological, chemical, and physical systems. The understanding of these systems is one of the major challenges facing physicists and a key issue in the community. Indeed, strongly correlated systems hold great potential in revolutionizing technological applications in medicine, communications, and computations. Within the framework of this project, novel extensions of a path-integral quantum Monte Carlo algorithm will be developed. The use of these Monte Carlo techniques will produce reliable and accurate results with controlled uncertainty. Unbiased theoretical predictions are timely and crucial to guide experimentalists in helping interpret experimental results and/or suggest observables. Moreover, the numerical results that will be obtained in this project can provide a platform for testing and validating analytical techniques. Indeed, these numerical techniques will also greatly contribute to the deeper understanding of certain classes of quantum many-body models which are, or will soon be, realizable in Atomic Molecular and Optical (AMO) experiments. In this project, the investigator and her students will develop extensions of quantum Monte Carlo techniques needed to study strongly-correlated many-body systems with an emphasis on cold polar molecules in optical lattice setups. When free of the sign problem, quantum Monte Carlo is a powerful theoretical tool to study equilibrium properties of strongly interacting systems, especially in dimensions higher than one. In this project the investigator will use the Worm algorithm to study properties of many-body strongly correlated systems of bosonic polar molecules trapped in optical lattice geometries. Emphasis will be given on geometries for which the anisotropic nature of the dipolar interaction will play a major role in determining the phase diagram of the system. The geometries that will be studied include stacks of one- and two-dimensional layers, and two-dimensional gases where molecules have tilted dipole moments. Considering the recent successful experimental advances in cold polar molecule experiments, these phases are very likely to be within reach in the near future. Therefore, accurate and reliable theoretical predictions are timely and valuable to the experimental community. The single-worm algorithm is not suitable to study the quantum phases of these multimers. In this project, the investigator plans to develop three different non-trivial extensions of the single-worm algorithm: (i) N-distinguishable-worms, (ii) N-indistinguishable-worms, and (iii) a hybrid algorithm with both distinguishable and indistinguishable worms. These multi-worm algorithms for quantum systems will allow for the study of multimer formation in a rich variety of optical lattice dipolar systems.

这个项目的目标是研究强关联系统的量子相位，重点是冷极性分子的设置。强相关性是许多迷人的生物、化学和物理系统的核心。对这些系统的理解是物理学家面临的主要挑战之一，也是社区的一个关键问题。事实上，强关联系统在医学、通信和计算领域的技术应用革命中具有巨大潜力。在这个项目的框架内，一个路径积分量子蒙特卡罗算法的新的扩展将被开发。使用这些蒙特卡罗技术将产生可靠、准确且不确定性可控的结果。无偏见的理论预测是及时和至关重要的指导实验学家在帮助解释实验结果和/或建议观察。此外，本计画所得到的数值结果，也可以提供一个分析技术验证的平台。事实上，这些数值技术也将大大有助于更深入地了解某些类别的量子多体模型，这些模型是，或将很快，实现在原子分子和光学（AMO）实验。在这个项目中，研究人员和她的学生将开发研究强相关多体系统所需的量子蒙特卡罗技术的扩展，重点是光学晶格设置中的冷极性分子。当没有符号问题时，量子蒙特卡罗是研究强相互作用系统，特别是高维系统平衡性质的有力理论工具。在这个项目中，研究人员将使用蠕虫算法来研究玻色子极性分子被困在光学晶格几何形状中的多体强关联系统的性质。重点将给予几何形状的偶极相互作用的各向异性性质将发挥重要作用，在确定系统的相图。将要研究的几何形状包括一维和二维层的堆叠，以及分子具有倾斜偶极矩的二维气体。考虑到最近在冷极性分子实验方面取得的成功进展，这些阶段很可能在不久的将来就可以实现。因此，准确可靠的理论预测对实验界来说是及时和有价值的。单蠕虫算法不适合研究这些多聚体的量子相。在这个项目中，研究人员计划开发三种不同的非平凡扩展的单蠕虫算法：（i）N-可区分的蠕虫，（ii）N-不可区分的蠕虫，和（iii）一个混合算法与可区分和不可区分的蠕虫。这些量子系统的多蠕虫算法将允许在各种各样的光学晶格偶极系统中的多聚体形成的研究。