Steady-State and Transient Properties of Strongly Correlated Single Molecule Junctions

加州大学圣地亚哥分校的Michael Galperin获得了化学系化学理论、模型和计算方法项目的奖项，以开发一种数值有效的计算方法来模拟远离平衡的强相关开放系统。现代量子材料的功能依赖于其基本构建块的性能：与周围环境相互作用的单个分子和原子。强关联系统作为一个具有挑战性的实验和理论问题吸引了越来越多的兴趣，为材料的基本行为提供了新的见解，并且因为它们作为量子技术中的构建块的潜在应用。近年来，STM单分子结与太赫兹（THz）光学探针的结合为单分子结中的原子尺度控制和时空成像提供了前所未有的可能性。将太赫兹扫描隧道显微镜应用于强关联单分子结只是时间问题。 目前，还没有理论方法可用于此类实验的第一原理建模：目前可用的理论方法要么有效地不相互作用，要么限制在其严格性和/或可访问的参数范围内，要么仅限于严格的一维系统，或者数值庞大。Galperin将开发适用于开放非平衡强相关系统在稳态和瞬态制度中的现实模拟的数值廉价但高度准确的方法，并将其应用于强相关单分子结的光谱建模。该项目的跨学科性质将是非常宝贵的，在发展学术课程的博士后和研究生，以及在吸引本科生进入research.The项目有助于多体绿色的功能方法和制定的杂质solvers和他们的实施领域，更复杂的（相比传统的）治疗是必要的发展。 开放系统的实际杂质求解器通常采用小参数的图解展开（例如，弱系统内相互作用或弱系统-浴耦合）。相应的选择方法是标准和赝粒子非平衡绿色函数（NEGF）技术，分别。在许多实验相关的情况下（特别是在强关联材料中），没有小参数可用于图解展开式的公式化。与此同时，不需要小参数存在的数值精确方法太笨重，无法用于现实模拟。 Michael Galperin将开发辅助量子主方程-对偶费米子（aux-DF）和对偶玻色子（aux-DB）方法作为可行的替代方案。该方法充分利用了对偶方法和辅助量子主方程技术的优点（不需要小参数和精确求解参考问题的能力），构造了一种新的杂质求解器。结构的理论允许实施开发的NEGF方法的时间依赖性过程中更复杂的强相关系统。具有高精度，精确的限制行为，和相对的数值负担能力aux-DF和aux-DB有可能成为一个计算工具的选择，在远离平衡的强相关系统的稳态和瞬态（超快）过程的研究。这一研究方向在概念上是新的，也是开放非平衡系统研究中从未采用过的方向。该奖项反映了NSF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。

Michael Galperin of the University of California, San Diego is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop a numerically efficient computational approach for simulation of strongly correlated open systems far from equilibrium. Functioning of modern quantum materials relies on performance of their elementary building blocks: single molecules and atoms interacting with their surroundings. Strongly correlated systems attract growing interest as a challenging experimental and theoretical problem providing new insights into fundamental behavior of materials and because of their potential application as building blocks in quantum technologies. Recently, combination of STM single-molecule junction with terahertz (THz) optical probe yields unprecedented possibilities of atom scale control and spatiotemporal imaging in single-molecule junctions. Application of the THz-STM to strongly correlated single-molecule junctions is only question of time. At the moment, there is no theoretical approach available for first principle modeling of such experiments: currently available theoretical approaches are either effectively non-interacting, or limited in their rigor and/or accessible parameter range, or restricted to strictly one-dimensional systems, or numerically heavy. Galperin will develop numerically inexpensive yet highly accurate methods suitable for realistic simulations in open nonequilibrium strongly correlated systems in steady-state and transient regimes and applies them in modeling spectroscopy of strongly correlated single-molecule junctions. The cross-disciplinary character of the project will be invaluable in developing academic curriculum for postdocs and graduate students, as well as in attracting undergraduates into research.The project contributes to development of many-body Green’s function methods and formulation of the impurity solvers and their implementation in areas where more sophisticated (compared to traditional) treatment is a necessity. Practical impurity solvers for open systems usually employ diagrammatic expansions in a small parameter (e.g., weak intra-system interaction or weak system-bath coupling). Corresponding methods of choice are the standard and pseudoparticle nonequilibrium Green’s function (NEGF) techniques, respectively. In many experimentally relevant situations (in particular, in strongly correlated materials) there is no small parameter to use in formulation of a diagrammatic expansion. At the same time, numerically exact methods, which do not require existence of a small parameter, are too heavy to be used in realistic simulations. Michael Galperin will develop auxiliary quantum master equation - dual fermion (aux-DF) and dual boson (aux-DB) methods as a viable alternative. The methods capitalize on strong sides of dual methodology and auxiliary quantum master equation technique (lack of necessity ion small parameter and ability to solve exactly reference problem , respectively) in formulation of a new impurity solver. Structure of the theory allows implementation of the developed NEGF methods for time-dependent processes in much more complicated strongly-correlated systems. With high accuracy, exact limiting behavior, and relative numerical affordability aux-DF and aux-DB have potential of becoming a computational tool of choice for studies of steady-state and transient (ultrafast) processes in strongly correlated systems far from equilibrium. This direction of research is conceptually new and the one which never was employed in studies of open nonequilibrium systems.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.