Novel Fractional Quantum Hall Effect and New Topological Phase in Interacting Systems

This project involves theoretical (numerical) approaches to the fundamental nature of new emerging quantum phases and associated topological and transport properties in several interacting systems. First, the Principal Investigator (PI), Dr. Donna Sheng at California State University Northridge, proposes to study outstanding issues related to the fractional quantum Hall effect (FQHE) in two dimensional electron systems in excited Landau level (LL), bilayer quantum wells, and graphene electron systems. A variety of new FQHE states have been recently discovered in suspended high quality graphene with unconventional sequence in favor of even numerators in Dirac LLs, potentially related to valley and spin degeneracies in such systems. The interplay of polarization of electron spins, competing between valley and spin correlations, and multi-orbital couplings remain not well understood for FQHE systems due to the complexity of the problem. Interestingly, these are systems with promising realization of two-component non-Abelian FQHE states. A large scale DMRG code with high accuracy has been developed by the PI and her collaborators, which can be used to study the bulk topological property, entanglement information, modular matrix, and edge transport to fully characterize new quantum phases. The proposed study aims at understanding existing experimental observations, characterizing the nature of quantum phases and their transitions, searching for microscopic conditions for realizing non-Abelian FQHE, and providing quantitative predictions regarding transport measurements for future experiments. Secondly, the PI proposes to study the new emerging fractionalized topological states for strongly interacting particles on different topological nontrivial bands without a magnetic field. They will explore the quantum phase diagram in realistic topological bands and address the interplay of interaction, nonuniform Berry curvature, and multi-component competition. They will characterize the nature of the quantum phases based on topological Chern number simulations and entanglement information, explore the edge and bulk correspondence, and search for new non-Abelian quantum phases. Such simulations will deepen our understanding of topological matter and provide valuable information for searching of new condensed matter or optical lattice systems for topological quantum computing. Thirdly, nontrivial topological states associated with the special band structure in electron systems with strong spin-orbit-coupling or under applied strain have stimulated intensive research activities in the past several years. A Z2 topological invariant is identified to distinguish a topological insulator from a trivial band insulator. The research goal in this direction is to identify some concrete examples of topologically ordered and fractionalized new quantum phases through tuning the interaction. They will predict transport properties of the new quantum phases, and suggest possible experimental detection of these phases based on large scale simulation and modeling of interacting systems. The scientific merit of this proposal lies in that topics addressed here are of fundamental importance for the understanding of new physical phenomena emerging in interacting systems, which are crucial for possible development of new magneto-electronics, and spintronic devices as well as topological quantum computing. Under DOE support, the PI and her collaborators have developed novel and effective numerical methods, based on topological invariant quantity and entanglement information to characterize emerging quantum phase and phase transition for interacting many-body systems. Thus the PI?s team believes that the proposed research can be carried out effectively and successfully. The present project will provide students and postdoctoral fellows with excellent training in solving challenging problems.