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We study the Hubbard model on the honeycomb lattice in the vicinity of thequantum critical point by means of a multiband formulation of the Dual Fermionapproach. Beyond the strong local correlations of the dynamical mean field,critical fluctuations on all length scales are included by means of a ladderdiagram summation. Analysis of the susceptibility yields an estimate of thecritical interaction strength of the quantum phase transition from aparamagnetic semimetal to an antiferromagnetic insulator, in good agreement toother numerical methods. We further estimate the crossover temperature to therenormalized classical regime. Our data imply that, at large interactionstrengths, the Hubbard model on the honeycomb lattice behaves like a quantumnonlinear sigma model, while being in a non-Fermi liquid state.

Multiband Dual Fermion Approach to Quantum Criticality in the Hubbard Honeycomb Lattice