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

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This project focuses on strongly correlated phases of cold-atomic systems in optical lattices where collective behavior is governed by laws of quantum mechanics. The prototypical strongly correlated fermionic systems -- the Hubbard model and resonant fermions in the regime of BCS-BEC crossover -- are central in the fields of the cold atom research and condensed matter. Understanding quantum plasticity and super transport in solid 4He remains one of big challenges in modern low-temperature physics. There is urgent need for universal unbiased first-principles methods for strongly correlated fermionic systems across all fields of physics, quantum chemistry, and materials science. Ab initio and model simulations provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions and help establish the proper theoretical framework, lay the ground for the unambiguous analysis of experimental data and further development of measuring techniques. In particular, this project aims to (i) develop generic diagrammatic Monte Carlo (DiagMC) tools for continuous-space and lattice fermionic/fermionized systems: resonant fermions, Hubbard model, and frustrated spin systems, (ii) understand quantum plasticity and supertransport in solid helium-4, (iii) perform Worm Algorithm (WA) studies of quantum-critical phenomena and novel phases of ultra-cold atoms: deconfined criticality, universal critical dynamics, phases of multi-bound complexes of polar molecules.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.