NSF-BSF: CDS&E: Tensor Train methods for Quantum Impurity Solvers

该奖项由美国-以色列NSF-BSF联合颁发。它支持旨在开发研究量子杂质模型的计算技术的研究。这些模型对于理解与更大环境耦合的小的、强相互作用的量子系统非常重要，例如宿主材料内的单个原子或与周围粒子相互作用的量子点。量子杂质可以表现出各种有趣的行为，包括根据其环境改变其电学或磁性。大多数量子杂质模型过于复杂，难以用传统的数学方法求解，特别是当它们涉及许多相互作用的部分且缺乏对称结构时。该项目的目标是推进我们现有的数字工具，以解决这些复杂的系统，并深入了解它们的性质。量子杂质模型也是计算材料电子特性和材料模型的更复杂技术的关键组成部分。这项国际合作产生的量子杂质求解器可能使计算材料电子性质的新技术成为可能，特别是那些涉及由强相互作用引起的相关电子运动的技术。这个项目产生的数字工具将广泛地提供给社区。该项目支持研究生在计算和理论材料研究方面的培训。面向公众的科学演讲将作为面向公众的周六上午物理推广活动的一部分。技术概述：该奖项支持用于各种目的的量子杂质求解器的开发。量子杂质求解器是一种数值算法，用于捕获由几个与环境耦合的强相互作用轨道组成的受限量子系统的“纠缠”或“相关性”。它们在从量子输运到近藤物理的应用中，以及在嵌入理论（如动态平均场和自能嵌入理论）的背景下都很重要。对于具有一般非对角线相互作用和杂质-槽杂化的杂质，缺乏精确和通用的量子杂质求解器是精确模拟量子多体系统的主要理论限制之一。这个美国-以色列NSF-BSF联合项目将探索量子杂质求解器的新型数据科学启发的张量收缩和压缩方案，建立在美国和以色列团体之间的长期合作基础上，旨在提供新一代量子杂质求解器，提供目前无法访问的参数空间区域。这项国际合作产生的量子杂质求解器可能使计算材料电子性质的新技术成为可能，特别是那些涉及由强相互作用引起的相关电子运动的技术。这个项目产生的数字工具将广泛地提供给社区。该项目支持研究生在计算和理论材料研究方面的培训。面向公众的科学演讲将作为面向公众的周六上午物理推广活动的一部分。这项国际合作产生的量子杂质求解器可能使计算材料电子性质的新技术成为可能，特别是那些涉及由强相互作用引起的相关电子运动的技术。这个项目产生的数字工具将广泛地提供给社区。该项目支持研究生在计算和理论材料研究方面的培训。面向公众的科学演讲将作为面向公众的周六上午物理推广活动的一部分。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award is made on a joint US-Israeli NSF-BSF. It supports research aimed to develop computational techniques for studying quantum impurity models. These models are important for understanding small, strongly interacting, quantum systems that are coupled to larger environments, such as a single atom inside a host material or a quantum dot interacting with surrounding particles. Quantum impurities can display various interesting behaviors, including changes in their electrical or magnetic properties, depending on their environment.Most quantum impurity models are too complicated to solve with traditional mathematical approaches, particularly when they involve numerous interacting parts and lack symmetrical structure. The goal of this project is to advance the numerical tools we have available to tackle these complex systems and gain a deeper insight into their properties. Quantum impurity models are also key components of more sophisticated techniques to calculate the electronic properties of materials and models of materials. Quantum impurity solvers resulting from this international collaboration may enable new techniques for calculating electronic properties of materials, particularly those involving correlated electron motion resulting from strong interactions. Numerical tools produced by this project will be made widely available to the community. The project supports the training of graduate students in computational and theoretical materials research. Science presentations for the general public will be developed as part of a Saturday Morning Physics outreach activity to the general public.TECHNICAL SUMMARYThis award supports the development of quantum impurity solvers for a variety of purposes. Quantum Impurity Solvers are numerical algorithms that capture the ‘entanglement’ or ‘correlation’ of confined quantum systems consisting of a few strongly interacting orbitals coupled to an environment. They are important both in their own right in applications ranging from quantum transport to Kondo physics, and in the context of embedding theories such as the dynamical mean field and self-energy embedding theories. The lack of accurate and generic quantum impurity solvers for impurities with general off-diagonal interactions and impurity-bath hybridization is one of the main theoretical limitations in the accurate simulation of quantum many-body systems. This joint US–Israeli NSF-BSF project will explore novel data-science-inspired tensor contraction and compression schemes for quantum impurity solvers, building on a long-standing collaboration between the US and the Israeli groups, with the aim of providing a new generation of quantum impurity solvers that provide access to areas of parameter space that are currently inaccessible. Quantum impurity solvers resulting from this international collaboration may enable new techniques for calculating electronic properties of materials, particularly those involving correlated electron motion resulting from strong interactions. Numerical tools produced by this project will be made widely available to the community. The project supports the training of graduate students in computational and theoretical materials research. Science presentations for the general public will be developed as part of a Saturday Morning Physics outreach activity to the general public.Quantum impurity solvers resulting from this international collaboration may enable new techniques for calculating electronic properties of materials, particularly those involving correlated electron motion resulting from strong interactions. Numerical tools produced by this project will be made widely available to the community. The project supports the training of graduate students in computational and theoretical materials research. Science presentations for the general public will be developed as part of a Saturday Morning Physics outreach activity to the general public.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.