This project seeks to understand, predict, and ultimately control the effects of correlations in quantum materials by developing a computational framework for controlled and unbiased studies of strongly interacting electron systems comprised of a diverse suite of complementary quantum many-body techniques. This framework will be designed to scale and perform efficiently on current petascale and future exascale computing architectures. Three specific aims are designed to reach this overarching goal. Specific aim (1), Advanced simulations of correlated quantum materials, focuses on controlled and reliable quantum many-body simulations using multiple techniques to study and understand the mechanisms leading to the complex phases and physical behavior observed in unconventional superconductors and quantum spin liquids. Specific aim (2), Development of accelerated algorithms and efficient implementations, develops improved algorithms based on state-of-the-art numerical methods to enable reliable studies of correlated systems in realistic but reduced models; and Specific aim (3), Tools for validation of simulations, focuses on developing improved procedures for accurately computing dynamical properties, enabling experimental verification and validation of the theoretical predictions.

A unique property of strongly correlated electron materials is the near degeneracy of different macroscopic states and their entanglement, which presents both opportunities and challenges. The opportunities range from new superconducting and magnetic materials to more efficient thermoelectric and new quantum information storage materials. The challenge is to understand the mechanisms responsible for their behavior and provide guidance in the design of this technologically important class of materials. This project develops and applies a set of advanced and complementary numerical techniques to calculate the properties of quantum spin-liquids and superconductors, two representative classes of correlated materials, and to determine the mechanisms responsible for their properties. The suite of algorithms includes dynamic cluster approximation, determinantal quantum Monte Carlo, and density matrix renormalization group methods, modern and established numerical techniques for the study of correlated systems. The project’s interdisciplinary team of condensed matter theorists, applied mathematicians, and computer scientists is guided by the objective to develop algorithms and application codes that scale and run efficiently on current and future high-performance computers. The importance of developing a complementary set of advanced algorithms and the use of high-end computing is related to the remarkable myriad of nearly degenerate quantum states in correlated systems and the limitations of the individual approaches. Only the combined application of different techniques, in conjunction with large-scale high-performance computing, will permit a complete, conclusive, and reliable picture of the physics of these systems. Central to this program is the calculation of dynamic susceptibilities and the 4-particle vertex that describes the scattering between two electrons. These quantities allow the team to address the question of what mechanism or mechanisms underlie the physical phenomena that are observed and how these predictions can be validated with experimental probes.