CAREER: Towards Predictive Modeling of Emergent Correlations and Dynamics in Strongly Interacting Quantum Matter

该职业奖支持理论和计算凝聚态物理的综合研究、教育和推广计划。该项目的主要目的是促进我们对由相互强烈相互作用的电子组成的量子物质的理解。这些系统是许多基本物理现象的核心，从磁性到超导性（无电阻的电子流动）。眼前的问题可以用一个日常生活中的类比来解释：一个人可能学会了弹奏单个音符，但不知道如何将它们组合在一起形成一个旋律。类似地，我们现在知道控制单个电子和原子核的量子力学定律，但发现很难预测许多此类相互作用组件的紧急行为。就像原子的集合根据外部条件将自己组织成固体、液体或气体一样，电子物质可以存在于“价键固体”、“量子自旋液体”或“费米气体”相，以及其他可能的相中。可靠地预测电子系统的行为将有助于未来的技术和寻找具有理想特性的量子材料。PI和他的团队将调查在自然界和世界各地的实验室中发现的几何“受挫”磁性材料。当电子“自旋”方向的多个空间排列各自具有相似的集体能量时，就会产生挫败感，因此没有明确的赢家。这一特征导致了在现代实验中观察到的不寻常的量子动力学，但理论解释有限。因此，该提案的主要重点是开发有效的计算机算法来预测这些量子材料在不同条件下（温度变化和磁场应用）的行为以及它们如何响应外部探测器（涉及光或中子）。PI和他的团队还将采用现有的最先进的数值方法来解决与这类磁性材料相关的突出的基本问题。PI的教育和推广项目与他的研究是协同结合的。重点是向研究生和更广泛的研究界传达量子系统计算方法的工作原理。根据专家作者的意见，PI和他的团队将编写一本电子书，训练下一代接受快速发展的量子力学概念词典。通过在他的家乡机构的多次推广活动，包括开放日和公共研讨会，PI将传达量子物理学在我们日常生活中的重要性。为了激励更多的学生追求更高的教育和科学事业，PI将在当地一所K-12学校开展辅导和指导活动，该学校招收了大量来自少数族裔的学生。该职业奖支持理论和计算凝聚态物理的综合研究、教育和推广计划。该项目的主要目的是促进我们对强相关量子系统的理解，这些系统不是由非相互作用的电子模型近似的。通过计算机模拟可靠地预测它们的行为仍然是物理、化学和材料科学的主要挑战。此外，时域相关系统的量子力学，平衡和非平衡现象的中心，不像它的时间独立对立物那样被很好地表征和理解。许多实验收集了大量的动态信息，但人们需要理论输入来解释它们。例如，从中子散射数据和理论的比较中间接推断出一维中自旋分馏的证据。PI和他的团队将研究几何上受挫的磁体，其中包含价键固体，量子自旋液体和自旋向列相。在这一领域的努力将进一步推动PI的目标，即在对量子材料了解最少的情况下，预测诸如转变温度、磁化曲线和动态响应等特性。PI和他的团队将在以下方向进行研究：他们将在外加磁场中对自旋轨道耦合、自旋冰和自旋1磁体在kagome和焦绿石晶格上的自旋动力学进行数值模拟和分析。将与非弹性中子散射和太赫兹光谱实验等动态探针测量结果进行比较。他们将探索一个包含“三色”精确基态的玩具格子模型。该模型提供了一种理解非平衡动力学现象（如玻璃性）的方法，并具有潜在的教学价值。他们将开发“密度矩阵向下折叠”技术，希尔伯特空间算子重整化的一种形式，以产生有效的哈密顿量。这种方法将有助于将真实材料与强相关的晶格模型联系起来。PI的教育计划将侧重于向研究生和更广泛的研究团体传达量子系统计算方法的工作原理。根据专家作者的意见，PI和他的团队将撰写一本电子书，重点关注基于多体波函数和密度矩阵的方法。通过在他的家乡机构的多次推广活动，包括开放日和公共研讨会，PI将传达量子物理学在我们日常生活中的重要性。为了激励更多的学生追求更高的教育和科学事业，PI将在当地一所K-12学校开展辅导和指导活动，该学校招收了大量来自少数族裔的学生。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 CAREER award supports an integrated research, education, and outreach program in theoretical and computational condensed-matter physics. The main aim of the project is to advance our understanding of quantum matter composed of electrons that interact strongly with one another. These systems are at the heart of many fundamental physical phenomena, ranging from magnetism to superconductivity (flow of electrons with no resistance). The problem at hand can be explained with an analogy from everyday life: one might learn to play individual musical notes yet not know how to put them together to produce a melody. Similarly, we now know the quantum-mechanical laws that govern individual electrons and nuclei but find it difficult to predict the emergent behavior of many such interacting components. Just as a collection of atoms organizes itself into a solid, liquid, or gas depending on external conditions, electronic matter can exist in "valence-bond solid," "quantum spin liquid," or "Fermi gas" phases, among other possibilities. Reliably predicting the behavior of electronic systems will aid future technologies and searches for quantum materials with desirable properties.The PI and his team will investigate geometrically "frustrated" magnetic materials found in nature and laboratories worldwide. Frustration arises when multiple spatial arrangements of electron "spin" orientations each have similar collective energy, so there is no clear winner. This feature results in unusual quantum dynamics that have been observed in modern-day experiments but for which theoretical explanations are limited. Thus, a major focus of this proposal is to develop efficient computer algorithms to predict how such quantum materials behave under different conditions (change in temperature and application of a magnetic field) and how they respond to external probes (involving light or neutrons). The PI and his team will also employ existing state-of-the-art numerical methods to address outstanding fundamental questions associated with this class of magnetic materials.The PI's education and outreach programs are synergistically coupled to his research. The focus is on communicating the workings of computational methods for quantum systems to graduate students and the wider research community. With input from expert authors, the PI and his team will write an e-book that will train the next generation to embrace a rapidly evolving lexicon of quantum-mechanical concepts. Through multiple outreach activities at his home institution, including open houses and public seminars, the PI will convey the importance of quantum physics in our everyday lives. To inspire more students to pursue higher education and careers in science, the PI will conduct tutoring and mentoring activities at a local K-12 school that enrolls a large number of students from underrepresented minority groups.TECHNICAL SUMMARYThis CAREER award supports an integrated research, education, and outreach program in theoretical and computational condensed-matter physics. The main aim of the project is to advance our understanding of strongly correlated quantum systems, those not approximated by a non-interacting model of electrons. Reliably predicting their behavior from computer simulations remains a major challenge in physics, chemistry, and materials science. Additionally, the quantum mechanics of correlated systems in the time domain, central to both equilibrium and non-equilibrium phenomena, is not as well-characterized and understood as its time-independent counterpart. Many experiments collect a wealth of dynamical information, but one needs theoretical inputs to interpret them. For example, evidence for fractionalized spinons in one dimension is indirectly inferred from comparison of neutron scattering data and theory.The PI and his team will investigate geometrically frustrated magnets, which harbor valence-bond-solid, quantum-spin-liquid, and spin-nematic phases. Efforts in this area will further the PI's goal of predicting properties such as transition temperatures, magnetization profiles, and dynamical responses, given minimal knowledge of the quantum material.The PI and his team will perform research in the following directions:1. They will numerically simulate and analyze spin dynamics at zero and finite temperature for spin-orbit-coupled, spin-ice, and spin-1 magnets on kagome and pyrochlore lattices in an applied magnetic field. Comparisons to measurements from dynamical probes such as inelastic neutron scattering and terahertz spectroscopy experiments will be carried out.2. They will explore a toy lattice model of frustration that harbors "three-colored" exact ground states. The model offers a way to understand non-equilibrium dynamical phenomena (such as glassiness) and has potential pedagogical value.3. They will develop the "density-matrix-downfolding" technique, a form of Hilbert-space operator renormalization, to generate effective Hamiltonians. This method will help connect real materials to strongly-correlated lattice models.The PI's education program will focus on communicating the workings of computational methods for quantum systems to graduate students and the wider research community. With input from expert authors, the PI and his team will write an e-book focused on many-body-wavefunction and density-matrix based approaches. Through multiple outreach activities at his home institution, including open houses and public seminars, the PI will convey the importance of quantum physics in our everyday lives. To inspire more students to pursue higher education and careers in science, the PI will conduct tutoring and mentoring activities at a local K-12 school that enrolls a large number of students from underrepresented minority groups.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.