Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo for strongly correlated condensed matter systems

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NONTECHNICAL SUMMARYThis award supports collaborative research and education on the collective quantum mechanical behavior of electrons in materials and of solid helium-4. The project is using and further developing two state-of-the-art computational approaches suitable for the study of quantum mechanical systems consisting of many interacting particles, the Worm Algorithm (WA) and Diagrammatic Monte Carlo (DiagMC), which were both introduced by the research team. With WA the team expects to advance understanding of striking properties demonstrated by imperfect crystals of helium-4 at low temperatures near the absolute zero of temperature, such as the frictionless transport of helium-4 atoms through the crystal, called supertransport, and an almost liquid-like response to an arbitrarily weak stress, called quantum plasticity. With DiagMC the team will address certain notoriously difficult problems concerning the behavior of many-electron systems, including the problem of how electrons develop the cooperative quantum mechanical state to become superconductors. Superconductors can conduct electricity without resistance.Understanding quantum plasticity, supertransport, and the interplay between them in solid helium-4 is a major challenge for modern low-temperature physics. More generally, there is an urgent need for universal methods suitable for describing the collective quantum behavior of electrons across all fields of physics, quantum chemistry, and materials science. The simulations at the core of the project provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions, help establish the proper theoretical framework, and provide foundation for the unambiguous analysis of experimental data and the further development of measuring techniques.An integral part of the project is the training of graduate students in advanced theoretical and numerical techniques, as well as in parallel computing. The project involves developing and maintaining a tutorial website on the numerical methods used, and the PIs plan to edit a book on the same, targeting a broad scientific audience. TECHNICAL SUMMARYThis award supports collaborative research and education on the collective quantum behavior of electrons in materials and of solid helium-4. The PIs will use and further develop two state-of-the-art Monte Carlo methods introduced by the research team: the Worm Algorithm (WA), and Diagrammatic Monte Carlo (DiagMC). The main goals of the project are: i) to use DiagMC for studying notoriously difficult condensed-matter problems such as: the Cooper instability in the fermionic repulsive Hubbard model including the possibility of high critical temperatures, modeling electronic systems with controlled ab initio treatment of long-range Coulomb and electron-phonon interactions, creating alternative formulations for strongly correlated models, and understanding the quantum-to-classical correspondence in frustrated spin models; ii) to carry out WA studies of disorder-induced quantum physics in solid He-4, such as supertransport and quantum plasticity associated with generic (tilted) dislocations.Understanding quantum plasticity, supertransport, and the interplay between them in solid helium-4 is a major challenge for modern low-temperature physics. More generally, there is an urgent need for universal methods suitable for strongly correlated fermionic systems across all fields of physics, quantum chemistry, and materials science. The simulations at the core of the project provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions, help establish the proper theoretical framework, and provide foundation for the unambiguous analysis of experimental data and the further development of measuring techniques.An integral part of the project is the training of graduate students in advanced theoretical and numerical techniques, as well as in parallel computing. The project involves developing and maintaining a tutorial website on the numerical methods used, and the PIs plan to edit a book on the same, targeting a broad scientific audience.