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

This RUI award supports theoretical research and education activities to investigate the fundamental nature of emerging quantum spin liquids, spin Bose metals, and non-Fermi liquids in frustrated magnetic materials and doped Mott insulator systems. The recent discoveries of unusual experimental properties of magnetic materials including Herbertsmithite kagome spin systems and triangular organic compounds serve as the impetus for this research. These systems have exhibited properties of possible spin liquids or non-Fermi liquids. The PI plans to study quantum phase diagrams and the topological nature of the gapped spin liquid in microscopic systems which may emerge in kagome and other lattice systems with geometric frustration and competing interactions. A systematic approach will be developed which can access different topological sectors, obtain entanglement information and the modular matrix to fully characterize the topological nature of the quantum spin liquid phase. The quantum phase diagram of a weak Mott insulator will be determined to identify the possible gapless spin liquid or non-Fermi liquid relevant for the organic compounds with Heisenberg exchange and ring-exchange interactions. The PI will develop a controlled and unbiased numerical approach to study gapless liquid phases in microscopic spin and electron models in quasi one-dimensional systems and scale to two-dimensions based on finite-size scaling analysis. The PI will also systematically study the nature of quantum phase transitions between these exotic quantum liquid states and other magnetically ordered or spatial symmetry broken states to search for the signature of a deconfined quantum criticality. In connection with experimental systems, the effect of additional realistic perturbations in materials will be systematically studied. Central to their computational approach, the PI and collaborators will continue developing a new density matrix renormalization group method that will find extensive applications for strongly interacting systems in both materials and ultra cold atom systesms.

The objectives of the research are to improve the theoretical understanding of the fundamental nature of new emerging quantum phases in these interacting systems, and to provide quantitative predictions and benchmark results based on numerical modelling for future theoretical and experimental studies.

In concert with this effort the PI hopes to develop new approaches and tools that will find extensive applications for strongly interacting systems in both materials and ultra cold atom systems. By further developing the PI's density matrix renormalization group algorithm, and incorporating matrix product states and tensor network renormalization, the exciting physics in these frustrated magnetic and doped Mott-insulator systems will be explored.

The research will be integrated with the education of undergraduate and graduate students. The project will provide students and postdoctoral fellows with training in solving challenging problems and in carrying out research at the forefront of condensed matter physics. It will also prepare and train minority and first generation students to be ready for the challenges they will face when they go on to their graduate study for the Ph.D. in physics or other science.