We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U = 0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

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Published in Physical Review Letters, v. 117, issue 8, 086404, p. 1-5.

© 2016 American Physical Society

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We acknowledge NSF DMR-1056536 (S. P. and R. K. K.), NSF DMR-1306897 (G. M.), U.S.–Israel BSF 2012120 (G. M.) for financial support, and NSF XSEDE DMR-150037, SuperMUC at Leibniz Supercomputing Centre and JURECA at Jülich Supercomputing Centre (JSC) for generous computer allocations.

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See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.117.086404 for more details on the perturbative generation of the linear kinetic term and associated RG flow, as well as additional simulation data and numerical tests.

bernal_sm.pdf (733 kB)
Supplemental Material