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.
This collaborative project supported by NSF, 2010-2013, was devoted to studying strongly interacting quantum states of matter -- superfluids, quantum solids as well as phases of ultracold gases of atoms and molecules. The main focus was on conducting large scale simulations of structural defects in the most quantum solid, Helium-4, and of trapped polar molecules. Significant part of the efforts has also been devoted to the numerical analysis of the non-standard paradigm of phase transformations --- so called Deconfined Critical Point (DCP). Solid Helium-4 continues puzzling researchers by its unusual properties for more than 50 years. In particular, some dislocations – linear defects of crystalline structure – in solid 4He have superfluid core so that atoms can flow without any resistance along it. With the help of Monte-Carlo simulations, we have found that imposing a small external stress on so called superclimbing edge dislocation can induce its roughening, so that it becomes able to climb with the help of the superflow along its core. Such roughening proceeds as a phase transition even at finite temperature which usually does not happen in 1D systems. One of the long-standing puzzles is how Helium-4 solidifies in narrow pores -- nanopores. Our first principle simulations have revealed that the solidification results in forming unusual topological structures. Ultracold trapped gases represent novel physical systems which have become a focus of intensive interdisciplinary research during last two decades. These systems are promising in several emerging areas of sciences and technologies. Our work has demonstrated that polar molecules (with fixed dipole moments) can form bound complexes which may become superfluid. In particular, it was found that in certain geometries there is an emergence of particles which don't exist in free space -- so called parafermions. These particles represent a generalization of fermions contemplated by Ettore Majorana almost 80 years ago. Potentially, these particles can be used in quantum computations. The standard paradigm of phase transitions was proposed by Lev Landau about 75 years ago and it was further developed by Vitaly Ginzburg, Kenneth G. Wilson and many other researchers. One of the main predictions is that no continuous phase transition can generically occur between phases of matter characterized by different symmetries. Instead, the transformation should proceed very much alike melting of water -- through coexistence of liquid and solid, that is, by discontinuous phase transition. This statement was challenged by the so called Deconfined Criticality conjecture about 10 years ago. The main idea of the conjecture is that there could be a sort of emerging variables which can continuosly transform generically unrelated symmetries one into another. A possible example of such phase transition was provided by so called J-Q model of quantum magnetism. In our work we have shown that the DCP conjecture correctly captures the critical behavior of the J-Q model only up to some intermediate sizes -- about 50-60 interatomic distances. Above this distance our numerical results find no evidence for the violation of the Ginzburg-Landau-Wilson paradigm, that is, the transition observed in the J-Q model between Neel anti-ferromagnet and the valence-bond solid is rather of discontinuous nature.
