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

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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.