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

RUI：有限温度下强相关材料的精确动力学特性

基本信息

批准号：
1918572
负责人：
Ehsan Khatami
金额：
$ 23.58万
依托单位：
San Jose State University Foundation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-12-01 至 2023-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1918572&HistoricalAwards=false
关键词：
RUI Exact Dynamical Properties Strongly

项目摘要

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.

该奖项支持开发用于模拟量子材料的数值方法的研究和教育。理解某些固体在低温下意想不到的、通常在技术上有用的特性背后的微观机制，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）关系的数值发现。尽管它们的动态（时间相关）相关性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立物更容易获得。例如，它们可以告诉我们系统对微小的外部扰动（包括电场或磁场）的反应。然而，我们常用的数值方法在处理动态特性时并不像处理静态特性那样可靠。在这个项目中，PI和他的团队将实现一个新颖的想法，在某些相互作用电子的数值模拟中更可靠地计算时间相关特性，从而产生精确的结果。他们将用这种方法来研究温度对性质的依赖，这些性质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这些系统的实验中的观察结果，并最终提高我们对物质转化为奇异相（如绝缘和超导相）背后机制的理解，并在技术、能源和运输部门得到应用。这些活动将为来自圣何塞州立大学不同人群的几名本科生提供在计算凝聚态物质、原子、分子和光学物理领域的实践研究经验。此外，学生将有机会通过撰写论文、发表论文和在国家会议上展示他们的发现来提高他们的科学交流技巧。该奖项还支持PI将其研究与本科教育相结合的努力。该奖项支持开发用于模拟量子材料的数值方法的研究和教育。探测相关材料的动力学特性，例如，它们对交变电场的反应，一直是理论上的挑战。我们最强大和最常用的晶格费米子数值方法，如基于蒙特卡罗的量子算法，也不能像静态算法那样有效可靠地处理依赖时间的相关性。该项目的目标是通过实时相关函数来扩展最先进的数值链接簇展开的适用性和性能，以研究自旋和电荷输运性质、谱函数和其他动态性质。后者将计算一组广泛使用的量子晶格模型，用于强相关电子系统，即费米-哈伯德，t-J和海森堡模型在一个和两个空间维度。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，有助于在光学晶格上的超冷费米子原子实验中表征系统。PI和他的团队计划采用其他技术，如时间依赖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。这些结果将阐明围绕强相关材料的动力学和输运性质的一些最具挑战性的问题，以及我们可以通过模型哈密顿量的量子模拟来理解它们的程度。这些活动将为来自圣何塞州立大学不同人群的几名本科生提供在计算凝聚态物质、原子、分子和光学物理领域的实践研究经验。此外，学生将有机会通过撰写论文、发表论文和在国家会议上展示他们的发现来提高他们的科学交流技巧。该奖项还支持PI将其研究与本科教育相结合的努力。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。