RUI: Theoretical (Numerical) Investigations of Novel Quantum Phases and Transitions in Strongly Interacting Systems

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TECHNICAL SUMMARYThis award supports research involving an extensive computational study of interacting boson and spin systems which are of fundamental importance in understanding strongly correlated many-body physics. The research aims for fundamental insights into that may be realized in ultracold atoms trapped in optical lattices and frustrated magnets.The PI aims to study boson Hubbard models with frustrated hopping and long range repulsions on triangular and other lattice systems to understand the microscopic conditions for realizing new quantum phases including different supersolid phases, a Mott-insulator, and possible spin-liquid phases. Such an investigation can result in quantitative predictions for the global phase diagram of interacting boson systems and reveal the nature of the quantum phase transitions which may belong to a new universality class. The PI will also study the spin liquid behavior, fractionalization, topological order and related quantum phase transitions in strongly correlated and frustrated magnetic systems. There are a growing number of magnetic materials discovered by experiment which exhibit candidate spin-liquid states. The PI will combine the exact Lanczos method with density matrix renormalization group methods to study the low energy spectrum, topological degeneracy, and spin-spin correlation function in various quantum spin models. The PI aims to gain fundamental insights and the research may establish ?proof of principle? evidence for the existence of novel spin liquid phases in simple spin models on kagome and square lattices aiming to make contact with experiments on Herbertsmithite and certain layered vanadium oxides and complex vanadium phosphates. This project supports educational experiences for students and postdoctoral researchers; minority students will be involved. The research contributes to a new computational course on many-body physics NON-TECHNICAL SUMMARYThis award supports computational research and education that will use advanced computational techniques to search for new electronic states of matter. The PI will study models for materials in which the smallest units of magnetism cannot simply align in such a way to become a magnet or an antiferromagnet. The interactions between neighboring smallest units of magnetism cannot be satisfied on the crystal lattice by any alignment. These frustrated magnets are candidates to exhibit new states of electronic matter. The PI aims to use computation to see whether specific theoretically proposed states of matter exist in models that are believed to be relevant to candidate materials, for example the mineral Herbertsmithite and high temperature superconductors.This is fundamental research that contributes to the intellectual foundations of our understanding of materials and new electronic states of matter that exhibit properties and exotic phenomena that lie outside our current understanding. This is an intellectual pursuit in its own right no less fascinating than the study of the universe, but it may also lead to the discovery of new phenomena and to contribute to future device technologies.This project supports educational experiences for students and postdoctoral researchers; minority students will be involved. The research contributes to a new computational course on many-body physics