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Z2 spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations

In a recent remarkable quantum Monte Carlo simulation of the hubbard model on honeycomb lattice, a spin disordered Mott insulator phase is discovered in the intermediate correlation regime. Using Projective Symmetry Group classification and physical arguments, we identify this spin liquid phase as the Sublattice-Pairing State (SPS) in the Schwinger-fermion representation. In addition, we show that SPS is identical to the zero-flux Z2 spin liquid in Schwinger-boson representation found
by Wang via an explicit duality transformation. SPS is connected to an unusual antiferromagnetic ordered phase, which we term as chiral-antiferromagnetic (CAF) phase, by an O(4) critical point. CAF phase breaks the SU(2) spin rotation symmetry completely and has three Goldstone modes. Our results indicate that there is
likely a hidden phase transition between CAF phase and simple AF phase at large U/t. We propose numerical measurements to reveal
the CAF phase and the hidden phase transition.