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

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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.