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The possibility to have a spin liquid (SL) phase, a novel quantum state of matter, in a realistic electronic model has been the recent subject of many theoretical studies in condensed matter physics. Among them, it has been reported that the half-filled Hubbard model on the honeycomb lattice, which is a canonical model for graphene, can have SL phase in a wide region of the ground-state phase diagram situated between the semi-metal (SM) and the antiferromagnetic insulator (AFMI) [1]. Since it is widely believed that not solely strong quantum fluctuations but also geometrical frustrations are responsible for stabilizing SL phase, the finding of SL phase in the unfrustrated honeycomb lattice is rather surprising, and thus has been one of the most debated issues in recent years. In addition, a similar SL phase have been claimed in the π-flux Hubbard model, whose non-interacting dispersion is also described by the Dirac fermions [2]. Taking a full advantage of K computer, we have re-examined the ground-state phase diagram of the Hubbard model on the honeycomb lattice as well as those of the π-flux Hubbard model with high accuracy by large-scale quantum Monte Carlo simulations. As opposed to the previous reports, our results strongly support a direct and continuous second order Mott transition between SM and AFMI both in the two lattice models [3,4]. We also discuss the quantum criticality of the Mott transition by finite-size scaling analysis.

[1] Z. Y. Meng et al., Nature 464, 847 (2010).
[2] C. Chang and R. T. Scalettar, Phys. Rev. Lett. 109, 026404 (2012).
[3] S. Sorrela, YO, and S. Yunoki, Sci. Rep. 2, 992 (2012).
[4] YO, S. Yunoki, and S. Sorella, J. Phys: Conf. Ser. 454, 012045 (2013).