Exotic physics in quantum Hall and spin liquid systems

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What are the possible phases of matter? This is a central question of condensed matter physics. Historically two organizing principles have been used: the free electron band theory and the theory of spontaneous symmetry breaking. A modern theme of quantum condensed matter physics is the quest to understand interacting many-body systems beyond these two paradigms. Two prominent examples are the fractional quantum Hall effect and quantum spin liquids. The most striking common feature of these systems is electron fractionalization: at low temperature the electrons behave as if they are "split" into smaller fractions (such as particles with fractional electric charge or statistics). This demonstrates the power of the principle of emergence: the collective behavior of a many-body system can be drastically different from its microscopic constituents. From a modern point of view electron fractionalization ultimately come from long-range quantum entanglement. My research program will be focused on better understanding various emergent phenomena due to long-range entanglement such as fractionalization.  In the next five years I would like to better understand (1) what are the allowed patterns of fractionalization in a given system? and (2) what are the effects of disorder on the physics of fractionalization? These questions are well motivated by recent experimental and theoretical developments. For example, a natural context for question (1) is to understand different possible patterns of fractionalization in a particularly interesting system known as the 5/2 quantum Hall state. An answer to this question would help establishing the 5/2 state unambiguously as a non-abelian topological order, potentially useful for future quantum information processing. Question (2) is motivated by the study of quantum spin liquids: during the past decade many "candidate" spin liquid materials have been discovered, but most of them tend to be rather dirty. An understanding of disorder effects in quantum spin liquids will therefore be crucial for bridging theories with experiments. The study of long-range quantum entanglement in many-body systems not only bears deep conceptual value on its own, but could also pave the way for future technological developments, ranging from quantum information processing to materials with previously unconceived electric properties - just like how the theories of free electrons and symmetry breaking laid the foundations for physics of semiconductors, magnets and superconductors, all of which played major roles in the technological revolution last century. This research program will train around four Ph.D. students. They will acquire various analytic and numerical skills in modern physics (such as those in quantum field theory, statistical mechanics and solid state physics). More importantly they will learn to think and communicate like physicists. All these will benefit their future career, in academia or in technology-related industry.