Invited Talk: Baigeng Wang
ORAL · Invited
Abstract
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.
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.
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Publication: 1. Rui Wang, Baigeng Wang, Tigran Sedrakyan, Phys. Rev. B 105, 054404 (2022).
2. Rui Wang, Zhiyan Xie, Baigeng Wang, Tigran Sedrakyan, Phys. Rev. B 106, L121117 (2022).
3. Rui Wang, Baigeng Wang, Tigran Sedrakyan, Phys. Rev. B 98, 064402 (2018).
4. Tao Yang, Banming Wang, Peng Song, Rui Wang, Baigeng Wang, Fermionic interpretation of the quantum phase transition in XXZ magnets, accepted by PRB.
5. Rui Wang, Yilin Wang, Y. X. Zhao, Baigeng Wang, Phys. Rev. Lett. 127, 237202 (2021).
Presenters
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Baigeng Wang
Nanjing Univ
Authors
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Baigeng Wang
Nanjing Univ