We use the Chern-Simons (CS) fermion representation of s=1/2 spin operators to construct topological, long-range magnetically ordered states of interacting two-dimensional (2D) quantum spin models. We show that the fermion-fermion interactions mediated by the dynamic CS flux attachment may give rise to Cooper pairing of the fermions. Specifically, in an XY model on the honeycomb lattice, this construction leads to a "CS superconductor", which belongs to a topologically nontrivial in 2D symmetry class DIII, with particle-hole and time-reversal symmetries. It is shown that in the original spin language, this state corresponds to a symmetry protected topological state, which coexists with a magnetic long-range order. We discuss physical manifestations of the topological character of the corresponding state.
Bibliographical noteFunding Information:
This work was supported by the PFC-JQI (T.S.), DOE-BES (DESC0001911) and Simons Foundation (V.G.), and DOE Contract No. DE-FG02-08ER46482 (A.K., T.S.). The work of T.S. and V.G. was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1066293.
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