CAREER: Entanglement, Pairing and Superfluidity at the Interface between Atomic and Nuclear Physics.

物理学的许多领域正在进入信息时代，计算处于研究的前沿。这个新时代的关键概念之一是纠缠的量子力学性质，它表征了量子粒子如何纯粹由于其量子力学性质而相互关联。粒子间相互作用对纠缠的影响是一个具有挑战性的问题，因为相互作用(特别是强相互作用)驱动相变，并对物质的有趣性质负责。与信息相关的量，如纠缠熵，在量子相变中扮演着至关重要的角色，并且是看似不同的领域的核心，如量子计算和黑洞。PI将利用原子、核物理和凝聚态物理方面的计算进展，以寻求对这些区域之间界面上强相互作用超流体系统的更深入了解，这些区域之间的纠缠性质在很大程度上仍未被探索。这个项目将提供纠缠的精确预测，以及它与广泛不同系统中的热力学观测数据的关联。研究生和本科生将在多个层次上参与，重点是正在进行的课程和与北卡罗来纳大学彭布罗克分校的跟踪开发合作。这个项目旨在准确描述与原子、分子和核物理相关的广泛的强耦合、非相对论、少数和多个费米子系统。这里考虑的系统将包括多个空间维度、自由空间、谐波陷阱和弱到强相互作用的区域。热力学性质(静态、动态、结构和配对关联)及其与纠缠的联系(纠缠熵、互信息)将使用非微扰方法来确定，包括数值格子场理论方法以及半解析展开(例如维里展开和算符乘积展开)。为此，将采用先进的计算方法和算法，并将探索计算纠缠熵的新途径。方法(代码、脚本、技术说明)和数据(从辅助现场配置到实物结果)将在网上提供。

Many areas in physics are entering an information age, with computation at the forefront of research. One of the key notions in this new era is the quantum-mechanical property of entanglement, which characterizes how quantum particles are correlated with each other purely as a result of their quantum-mechanical nature. The influence of inter-particle interactions on entanglement is a challenging question, as interactions (in particular strong ones) drive phase transitions and are responsible for intriguing properties of matter. Information-related quantities, such as the entanglement entropy, play an essential role in quantum phase transitions and are central to seemingly disparate areas, such as quantum computation and black holes. The PI will leverage computational progress in atomic, nuclear and condensed matter physics to pursue a deeper understanding of strongly interacting superfluid systems at the interface between those areas, where entanglement properties remain largely unexplored. This project will provide precise predictions of entanglement and its correlation with thermodynamic observables across a wide variety of systems. Graduate and undergraduate students will be engaged at multiple levels, with emphasis on an ongoing curriculum and track-developing collaboration with the University of North Carolina at Pembroke.This project aims for a precise characterization of a wide range of strongly coupled, non-relativistic, few- and many-fermion systems of relevance to atomic, molecular, and nuclear physics. The systems considered here will include multiple spatial dimensions, free space, harmonic traps, and weakly to strongly interacting regimes. Thermodynamic properties (static, dynamic, structural, and pairing correlations) and their connection to entanglement (entanglement entropies, mutual information) will be determined using non-perturbative approaches, including numerical lattice field theory methods as well as semi-analytic expansions (e.g. the virial and operator-product expansions). To this end, advanced computational methods and algorithms will be implemented and new approaches will be explored to calculate entanglement entropies. The methods (codes, scripts, technical notes) and the data (from auxiliary field configurations to the physical results) will be made available online.