Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice

Abstract

We address the nature of the antiferromagnetic quantum phase transition that separates a semimetal from an antiferromagnet in the repulsive Hubbard model defined on the honeycomb lattice. At the critical point, the fermions acquire an anomalous dimension $\eta$ due to their strong coupling to the fluctuations of the order parameter $\varphi$. The finite $\eta$ in turn induces a singular ${\varphi }^4$ term and a non-analytical spin susceptibility signaling the breakdown of Hertz's ${\varphi }^4$ theory. As a result, the continuous antiferromagnetic quantum phase transition is internally unstable and turns into a first order transition.

arXiv comment4 pages, 3 figures

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