This award supports theoretical research and education on fractionalized spin liquid phases in frustrated quantum magnets. The research is stimulated by recent discoveries of several candidate spin liquid materials with spins residing on two-dimensional and three-dimensional lattices. The PI aims to expand the available toolbox of wave functions for such fractionalized phases using a parton approach. In this approach, the microscopic spin or boson operator is split into auxiliary quark-like fields, which are taken to be deconfined in mean field and are then glued together by a projection recovering the physical Hilbert space. Besides popular Gutzwiller-projected slave fermion states, the PI will also use projected Schwinger boson wave functions that are strong candidates near magnetically ordered phases, as well as novel wave functions motivated from Majorana slave fermion approaches that can further enrich the pool of states with gapless spinons. Another interesting direction is possible combination with novel entanglement-based numerical approaches.
In a separate thrust, the PI will work to develop a better understanding of gapless fractionalized phases where the emergent gauge fields are also gapless, which are some of the most challenging cases where analytical approaches are not under full control. The PI will build upon an example of an Exciton Bose Liquid phase in models with pure ring exchanges, where the parton-gauge approach can be brought to completion and also compared with non-parton approaches. The study will address a number of open questions in the Exciton Bose Liquid theory and will use these to learn about gapless parton-gauge systems.
The PI will also explore unusual phase transitions in statistical mechanics problems with topological terms, combining analytical duality approaches and numerical Monte Carlo techniques in a powerful way. The focus will be on models with particles that have mutual statistical interactions. Such models arise in studies of topological phases and their phase transformations and also in effective field theories of frustrated quantum antiferromagnets. The research will help to understand unconventional quantum phase transitions of much recent interest.
NON-TECHNICAL SUMMARY This award supports theoretical research and education focusing on unusual quantum states of matter that show a kind of fractionalization phenomenon. In a sense, electrons are like tiny spinning tops quantified in the term spin. They also carry a unit of electric charge. Fractionalization results when electrons appear to behave as though they were split into two independent particles, one that has electric charge but has no spin and one that has spin but no charge. Fractionalization was discovered experimentally for electrons constrained to move in a plane in a semiconductor interface and exposed to strong magnetic field. Similar phenomenon had long been conjectured to occur naturally in materials. Recently several candidates were found. This project aims to develop theoretical and computational toolbox to discover and characterize fractionalized quantum phases in models and experimental materials. It will also study transformations that can occur among such states that lie outside the standard theory of phase transitions.
The discovery of new quantum states of electronic matter in materials may lead to new technologies. The manipulation of some quantum states of electronic matter may lead to a new way to do computation, quantum computing, that would be potentially more powerful than existing computers.
