Invited Talk: Baigeng Wang

Chern-Simons fermionization approach to correlated quantum spin systems

Correlated spin systems host rich many-body phenomena, including long-range magnetic orders, quantum spin-liquids, topological phase transitions, and quantum criticalities. It is of crucial importance to look for general theories describing these quantum phenomena within the same framework. We develop a general method to study correlated quantum spin systems, namely, the lattice Chern-Simons (CS) fermionization approach. We introduce a systematic mapping scheme, which transforms the quantum spin models into low-energy effective theories describing interacting spinless CS fermions. We show that the mean-field theories based on the CS fermions well describe different types of long-range magnetic orders, which further lead to field theoretical descriptions of the quantum phase transitions between them. With further considering the quantum fluctuations beyond the mean-field level, the approach can make predictions about certain quantum spin-liquids in frustrated quantum magnets. Correspondingly, new understandings are obtained for the topological phase transitions between long-range magnetic orders and quantum spin liquids. Furthermore, the method is also applicable to other correlated systems, for example, the quantum impurity problems in spin-liquids, where it indicates the emergence of Kondo physics induced by gauge fluctuations. These results suggest that the lattice CS mean-field theory could provide a general framework for studying correlated spin systems.