In a Schwinger-fermion representation we classify all 128 possible spin liquids that preserves
SU(2) spin-rotational symmetry, honeycomb lattice group symmetry, and time-reversal symmetry. Among them we identify a
Z2 spin liquid called the sublattice-pairing state (SPS) as the spin liquid phase discovered in recent numerical study on a honeycomb lattice [Meng et al., Nature (London) 464, 847 (2010)]. Our method provides a systematic way to identify spin liquids close to Mott transition. We also show that the SPS is identical to the zero-flux
Z2 spin liquid in Schwinger-boson representation [Wang, Phys. Rev. B 82, 024419 (2010)]. through an explicit duality transformation. SPS is connected to an unusual antiferromagnetic ordered phase, which we term the chiral-antiferromagnetic (CAF) phase, by an
O(4) critical point. The CAF phase breaks the
SU(2) spin rotational symmetry completely and has three Goldstone modes. Our results indicate that there is likely a hidden phase transition between the CAF phase and the simple antiferromagnetic phase at large
U/t. We also propose numerical measurements to reveal the CAF phase and the hidden phase transition.
The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin-
21 fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.
Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.