CAREER: Detecting and Designing Topological Orders in Frustrated Magnets

Ohio State University, The, Columbus OH

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education towards developing new ideas to detect and design topological orders in quantum magnetic materials. Topological orders are exotic phases of quantum systems, in which ordinary electrons behave as if they were divided into smaller particles that contain fractions of the original mass and charge. These emerging particles are called anyons, and due to their quantum properties they could be used in implementing quantum computation. One example of topological order is the so-called quantum spin liquid, a nonmagnetic phase of matter that can emerge in systems of interacting quantum magnets. While topological orders are highly desirable for their potential applications, there are two longstanding obstacles in achieving control of anyons: (i) anyons in topological orders are hard to detect; (ii) topological orders are quite rare in nature to begin with. This project aims at filling those two gaps in the context of quantum spin liquids. The PI will exploit magnetic impurities that are ubiquitous in real materials to identify a "smoking gun" signature for the detection of anyons in a quantum spin liquid. The PI will also identify new guiding principles to search for realistic models of and materials hosting quantum spin liquids, by building a road map between rare quantum spin liquids and abundant magnetic orders in nature. These research efforts not only bring new ideas for the detection and realization of topological orders, but also shed new light on impurity physics in various quantum magnetic materials. This award also supports educational and outreach efforts that are integrated with the research. In addition to mentoring graduate students and developing modern courses synergistically with the research activities, the PI will also mentor master's degree students from underrepresented groups, involving them in cutting-edge research. Outreach activities will include constructing an interactive website about the PI's research, and educating underrepresented K-5 level students in high-poverty elementary schools with demonstration-based lectures. TECHNICAL SUMMARY This CAREER award supports theoretical research and education towards detecting and designing quantum spin liquid phases in frustrated magnetic systems. Quantum spin liquids are exotic ground states of frustrated magnets, which evade all symmetry-breaking orders down to zero temperature. They can support topological orders featuring fractionalized excitations (anyons), which could become building blocks for fault-tolerant topological quantum computation. Though highly desirable, the experimental detection of anyons in quantum spin liquids has been a longstanding challenge. Moreover, the rarity of quantum spin liquids in nature calls for new design principles. This project will address these two significant issues. The PI will address the detection issue by answering the following question: is there a "smoking gun" signature of anyons in quantum spin liquids? Magnetic impurities will be explored as a means to provide sharp signatures of anyons, which could subsequently be probed by thermodynamic and spectroscopic measurements in real materials. The effects of magnetic impurities in quantum spin liquids will be investigated by a synergy between analytical effort, numerical simulation, and exact solutions from idealized models. The PI will also address the design issue by constructing new models that host quantum spin liquid ground states. This will be achieved by combining an algebraic classification of symmetry-breaking orders in proximity to quantum spin liquids with unbiased numerical simulations. New classes of quantum criticality between a quantum spin liquid and proximate symmetry-breaking phases will also be investigated. This award also supports educational and outreach efforts that are integrated with the research. In addition to mentoring graduate students and developing modern courses synergistically with the research activities, the PI will also mentor master's degree students from underrepresented groups, involving them in cutting-edge research. Outreach activities will include constructing an interactive website about the PI's research, and educating underrepresented K-5 level students in high-poverty elementary schools with demonstration-based lectures.