Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo for Strongly Correlated Condensed Matter Systems

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NONTECHNICAL SUMMARYThis award supports theoretical and computational research with an aim to advance fundamental understanding of materials in which electrons interact strongly with each other. These materials exhibit unusual properties and phenomena which may lead to future device technologies. The PIs will use advanced computational approaches they have developed to perform computer simulations of electrons in this class of materials, and to explore the properties of a conceptually related system of strongly interacting particles - helium atoms at very low temperatures and modest pressure. The team will use simplified models to investigate how superconductivity can occur in materials with strongly interacting electrons. Superconductivity is a quantum state of matter where the electrons act in concert. A consequence is that electrons in a superconducting state can flow without resistance, unlike those in copper and the metals from which heating elements are made. The team will also investigate novel states of electrons that emerge due to their interaction with the vibrations of the crystalline lattice. The team will further pursue the consequences of interactions of strongly interacting electrons with crystalline lattice vibrations and investigate novel states that emerge when crystals are illuminated by light. Another focus of the project is helium, the second lightest element, which is in gas phase at room temperature. At extremely low temperatures helium becomes a liquid that can be thought of as a strongly interacting system of electrons, but without charge. At pressures above 25 times the atmospheric pressure, it becomes a crystalline solid and, like the liquid, displays intriguing properties consistent with the principles of quantum mechanics applied to systems of many interacting particles. At sufficiently low temperatures, liquid helium enters a state, called superfluidity, which is the analog of superconductivity. The team will explore striking properties of imperfect crystals of helium that arise as a consequence of quantum mechanics and the light mass of helium atoms. These include the frictionless transport of helium atoms through the solid and puzzling plastic phenomena observed in experiments for which no satisfactory theoretical explanations currently exist. The research team is well positioned to advance knowledge in these challenging problems of fundamental and technological interest, in part because the computational tools they have developed are well suited for the investigation of systems with strongly interacting particles, such as electrons in some classes of materials and helium atoms at extremely cold temperatures and modest pressures.This project also supports training graduate student and post-doctoral researchers in advanced numerical techniques, quantum statistics, topical problems of condensed-matter and atomic physics, and high-performance computing. This project also helps to advance the Precision Many Body Physics Initiative which is aimed to facilitate international collaboration in cutting edge research directed toward understanding collective properties of matter, including quantum matter. Activities planned within this context include: two major international workshops, Focused Sessions at American Physical Society March Meetings, and topical mini workshops at UMass Amherst.TECHNICAL SUMMARYThis award supports theoretical and computational research aimed at achieving a fundamental understanding of electronic and transport properties of a variety of condensed matter systems through the use of two state-of-the-art first-principles approaches to correlated quantum many-body systems: Worm Algorithm (WA) and Diagrammatic Monte Carlo (DiagMC); both introduced by the research team. The main goals of the project are: (i) DiagMC studies of Cooper instability in prototypical models of correlated electrons: systems with Coulomb and electron-phonon interactions and the repulsive Fermi-Hubbard model. (ii) DiagMC study of novel polaron states. (iii) WA-based study of disorder-induced quantum physics in solid He-4. (iv) WA-based study of novel exciton-photonic cooperative phases.This project also supports training graduate student and post-doctoral researchers in advanced numerical techniques, quantum statistics, topical problems of condensed-matter and atomic physics, and high-performance computing. This project also helps to advance the Precision Many Body Physics Initiative which is aimed to facilitate international collaboration in cutting edge research directed toward understanding collective properties of matter, including quantum matter. Activities planned within this context include: two major international workshops, Focused Sessions at American Physical Society March Meetings, and topical mini workshops at UMass Amherst.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.