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Quantum spin liquid emerging in two-dimensional correlated Dirac fermions


At sufficiently low temperatures, condensed-matter systems tend to develop order. A notable exception to this behaviour is the case of quantum spin liquids, in which quantum fluctuations prevent a transition to an ordered state down to the lowest temperatures. There have now been tentative observations of such states in some two-dimensional organic compounds, yet quantum spin liquids remain elusive in microscopic two-dimensional models that are relevant to experiments. Here we show, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence-bond liquid, akin to the one proposed for high-temperature superconductors: the possibility of unconventional superconductivity through doping therefore arises in our system. We foresee the experimental realization of this model system using ultra-cold atoms, or group IV elements arranged in honeycomb lattices.

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Figure 1: Phase diagram for the Hubbard model on the honeycomb lattice at half-filling.
Figure 2: Finite-size extrapolations of the excitation gaps and the antiferromagnetic structure factor.
Figure 3: Derivative d Ekin/d U of the kinetic energy density as a function of U/t for systems of different sizes.
Figure 4: Real-space plot of the spin dimer–dimer correlations.


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We thank L. Balents, S. Capponi, A. H. Castro Neto, A. Georges, M. Hermele, A. Läuchli, E. Molinari, Y. Motome, S. Sachdev, K. P. Schmidt and S. Sorella for discussions. We are grateful to S. A. Kivelson for thoroughly reading our manuscript and providing important suggestions. F.F.A. is grateful to the Kavli Institute for Theoretical Physics of the University of California, Santa Barbara, for hospitality and acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) through grants AS120/4-3 and FG1162. A.M. thanks the Aspen Center for Physics for hospitality and acknowledges partial support by the DFG through grant SFB/TRR21. S.W. acknowledges support by the DFG through grants SFB/TRR21 and WE3649. We thank the John von Neumann Institute for Computing, Jülich; the Hochleistungsrechenzentrum, Stuttgart; the BW Grid; and the Leibniz-Rechenzentrum, München, for the allocation of CPU time.

Author Contributions F.F.A. developed the simulation codes; Z.Y.M. and T.C.L. performed the simulations and analyses and prepared the figures; F.F.A., A.M. and S.W. directed the investigation and wrote the paper. The manuscript reflects the contributions of all authors.

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Correspondence to Z. Y. Meng.

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This file contains Supplementary Discussions which comprises: 1 Green's function and single particle gap; 2 Spin correlations and SAF; 3 Spin excitation gaps; 4 Density correlations; 5 Dimer-dimer correlations - charge sector; 6 Dimer-dimer correlations - spin sector, 7 Flux quantization measurement for superconductivity; 8 Order parameters for superconductivity and it also includes Supplementary Figures 1-11 with legends. (PDF 438 kb)

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Meng, Z., Lang, T., Wessel, S. et al. Quantum spin liquid emerging in two-dimensional correlated Dirac fermions. Nature 464, 847–851 (2010).

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