RUI: Exact Dynamical Properties of Strongly Correlated Materials at Finite Temperatures

非技术总结该奖项支持为量子材料模拟开发数值方法的研究和教育。了解某些固体在低温下意外的、往往在技术上有用的性质背后的微观机制，在很大程度上依赖于简化模型中电子之间静态(与时间无关)关系的数值结果。尽管它们的动态(与时间相关的)关联有时可以提供对系统状态的更直接的了解，并且在实验中比它们的静态对应关系更容易获得，但这是事实。例如，它们可以告诉我们系统对微小的外部扰动的反应，包括电场或磁场。然而，我们常用的数值方法并不像静态方法那样可靠地处理动力学性质。在这个项目中，Pi和他的团队将在某些相互作用电子的数值模拟中实现一个新的想法，以更可靠地计算与时间相关的性质，从而产生准确的结果。他们将使用这种方法来研究性质与温度的关系，这可以告诉我们电子的集体重排和它们可能经历的不同转变。这些结果将有助于解释模拟此类系统的实验中的观察结果，并最终将提高我们对物质转变为奇异相(如绝缘相和超导相)背后的机制的理解，以及在技术、能源和交通领域的应用。这些活动将为圣何塞州立大学不同人群的几名本科生提供计算凝聚态以及原子、分子和光学物理领域的实践研究经验。此外，学生们将有机会通过撰写论文、发表论文并在全国会议上展示他们的发现来提高他们的科学交流技能。该奖项还支持PI将他的研究与本科教育相结合的努力。技术总结该奖项支持开发量子材料模拟的数值方法的研究和教育。探索相关材料的动力学性质，例如它们如何响应交变电场，一直是理论上的挑战。我们最强大和最常用的格点费米子数值方法，如基于量子蒙特卡罗的算法，也没有被设计成像它们的静态对应那样有效和可靠地处理依赖于时间的关联。这个项目的目标是通过实时关联函数来扩展最先进的数值链接团簇展开的适用性和性能，以研究自旋和电荷输运性质、谱函数和其他动力学性质。对于强关联电子系统的一组广泛使用的量子晶格模型，即一维和二维的Fermi-Hubbard模型、t-J模型和Heisenberg模型，将计算后者。该方法直接在热力学极限下工作，并将用于在有限温度下获得结果，这对于在光学晶格上进行超冷费米子原子实验中的系统表征是有用的。Pi和他的团队计划使用其他技术，如依赖于时间的密度矩阵重整化群和行列式量子蒙特卡罗，用于基准测试和交叉验证，并在不同数值方法的结果之间建立共识。这一结果将揭示一些围绕强关联材料的动力学和输运性质的最具挑战性的问题，以及我们可以在多大程度上通过模型哈密顿的量子模拟来理解它们。这些活动将为圣何塞州立大学不同人群的几名本科生提供计算凝聚态以及原子、分子和光学物理领域的实践研究经验。此外，学生们将有机会通过撰写论文、发表论文并在全国会议上展示他们的发现来提高他们的科学交流技能。该奖项还支持了PI将他的研究与本科教育相结合的努力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 supports research and education on developing numerical methods for the simulation of quantum materials. Understanding the microscopic mechanisms behind unexpected and often technologically useful properties of certain solids at low temperatures has largely relied on numerical findings for static (time-independent) relationships between electrons in simplified models. This is despite the fact that their dynamical (time-dependent) correlations can sometimes offer more direct insight into the state of the system and be more readily accessible in experiments than their static counterparts. For example, they can tell us about the reaction of a system to small external perturbations, including electric or magnetic fields. Our commonly used numerical methods, however, are not designed to deal with dynamical properties as reliably as with static ones.In this project, the PI and his team will implement a novel idea for more reliable calculations of time-dependent properties in certain numerical simulations of interacting electrons that yield exact results. They will use the method to study the temperature dependence of properties that can tell us about the collective rearrangements of electrons and the different transformations they can undergo. The results will help interpret observations in experiments that emulate such systems and will ultimately improve our understanding about the mechanism behind transformation of matter into exotic phases, such as insulating and superconducting phases, with applications in the technology, energy, and transportation sectors. The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the fields of computational condensed-matter and atomic, molecular, and optical physics. In addition, the students will have opportunities to improve their scientific communication skills through writing papers, publishing them, and presenting their findings in national meetings. The award also supports the PI's efforts towards integrating his research with undergraduate education.TECHNICAL SUMMARYThis award supports research and education on developing numerical methods for the simulation of quantum materials. Probing dynamical properties of correlated materials, for example, how they respond to an alternating electric field, has always been challenging for theory. Our most powerful and commonly used numerical methods for lattice fermions, such as quantum-Monte-Carlo-based algorithms, are also not designed to deal with time-dependent correlations as efficiently and reliably as their static counterparts. The goal of this project is to expand the applicability and performance of the state-of-the-art numerical linked-cluster expansions to study spin- and charge-transport properties, spectral functions, and other dynamical properties through real-time correlation functions. The latter will be calculated for a set of widely-used quantum lattice models for strongly-correlated electronic systems, namely, the Fermi-Hubbard, t-J, and Heisenberg models in one and two spatial dimensions. The method works directly in the thermodynamic limit and will be utilized to obtain results at finite temperatures, useful for characterizing systems in experiments with ultracold fermionic atoms on optical lattices. The PI and his team plan to employ other techniques, such as the time-dependent density-matrix renormalization group and determinant quantum Monte Carlo, for benchmarking and cross-validation, and for building consensus among results from different numerical methods. The results will shed light on some of the most challenging questions surrounding the dynamics and transport properties of strongly-correlated materials and the extent to which we can understand them through quantum simulations of model Hamiltonians. The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the fields of computational condensed-matter and atomic, molecular, and optical physics. In addition, the students will have opportunities to improve their scientific communication skills through writing papers, publishing them, and presenting their findings in national meetings. The award also supports the PI's efforts towards integrating his research with undergraduate education.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.