Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo in Atomic and Condensed Matter Physics

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This project focuses on ultra-cold atoms and quantum crystals where collective behavior is governed by laws of quantum mechanics. Understanding these systems is crucial for theoretical modeling, condensed matter physics, and materials science because of the prospects for discovering new states of matter. One of such states --- supersolidity of Helium-4 --- remains one of the biggest puzzles in the modern low-temperature physics. One finds interacting quantum systems across all fields of physics, quantum chemistry, and materials science and there is urgent need for universal unbiased first-principles methods to deal with them in their full complexity. This project is aimed at developing such methods, with the particular focus on: (i) Studying collective phenomena in disordered, multi-component, and other non-trivial cold-atomic ensembles in optical lattices and in continuous space, including interacting fermions in the crossover regime with physics intermediate between that of conventional superconductors and bosonic superlfuids; (ii) Understanding the microscopic picture behind and novel phenomena associated with the supersolidity in Helium-4; (iii) Advancing Monte Carlo techniques and algorithms as a universal tool for solving quantum-statistical problems - diagrammatic Monte Carlo for fermions and Worm Algorithm for bosons.An unbiased theoretical description of collective quantum phenomena is of vital interdisciplinary importance for a number of applied and fundamental areas, such as quantum computing and high-energy physics. High-end computing methods and techniques often find applications outside the physics community. Simulations of complex models with multiple constraints, randomness, and a variable number of continuous parameters are typical in polymer science, neural networks, computer science, behavioral, social and economics studies. The algorithms developed in the project provide an example of how some of the difficulties may be circumvented. An integral part of the project is the training of graduate students and post-doctoral associate in advanced numeric techniques, quantum statistics, topical problems of atomic and solid state physics, network administration, and parallel supercomputing. This project includes: (i) developing tools for visualizing quantum statistical phenomena in terms of Feynman's paths (worldlines) and diagrams; (ii) maintaining an interactive web site popularizing, teaching and disseminating new algorithms and codes; (iii) upgrading and administrating major shared computational facilities at both Universities; (iv) developing and teaching a multi-institutional graduate tele-course on advanced numeric methods; (v) writing a book on superfluid states of matter and developing on its basis a graduate course; (vi) promoting higher standards in science education at schools; (vii) organizing a workshop on supersolidity.