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

这个项目的目标是研究强相关系统的量子相，重点是冷极性分子设置。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，也是科学界的一个关键问题。事实上，强相关系统在医学、通信和计算领域的革命性技术应用方面具有巨大的潜力。在这个项目的框架内，路径积分量子蒙特卡罗算法的新扩展将被开发。使用这些蒙特卡罗技术将产生可靠和准确的结果，不确定性可控。无偏的理论预测是及时和至关重要的，以指导实验者帮助解释实验结果和/或提出观察结果。此外，本项目将获得的数值结果可以为测试和验证分析技术提供一个平台。事实上，这些数值技术也将极大地有助于更深入地理解某些类别的量子多体模型，这些模型已经或将很快在原子分子和光学（AMO）实验中实现。在这个项目中，研究者和她的学生将开发量子蒙特卡罗技术的扩展，以研究强相关的多体系统，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平衡性质的有力理论工具，特别是在大于1维的情况下。在这个项目中，研究者将使用Worm算法来研究被困在光学晶格几何中的玻色子极性分子的多体强相关系统的性质。重点将放在几何上，其中偶极相互作用的各向异性性质将在确定系统的相图中起主要作用。将被研究的几何形状包括一、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中成功的实验进展，这些相很可能在不久的将来触手可及。因此，准确可靠的理论预测对实验界来说是及时而有价值的。单蠕虫算法不适合研究这些多定时器的量子相位。在这个项目中，研究者计划开发单蠕虫算法的三种不同的非平凡扩展：(i) n-可区分蠕虫，（ii） n-不可区分蠕虫，以及（iii）可区分蠕虫和不可区分蠕虫的混合算法。这些用于量子系统的多蠕虫算法将允许在丰富多样的光学晶格偶极系统中研究多时间形成。

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.