Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice

TL;DR

This paper investigates the antiferromagnetic quantum phase transition on the honeycomb lattice, revealing it becomes first order due to strong fermion fluctuations and breakdown of traditional theories.

Contribution

It demonstrates that the antiferromagnetic transition in the Hubbard model on the honeycomb lattice is inherently first order, challenging previous continuous transition assumptions.

Findings

Fermions acquire an anomalous dimension at criticality

Singular $^{4}$ term indicates breakdown of Hertz's theory

Transition becomes first order due to strong coupling effects

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 $\phi$. The finite $\eta$ in turn induces a singular $\phi^{4}$ term and a non-analytical spin susceptibility signaling the breakdown of Hertz's $\phi^{4}$ theory. As a result, the continuous antiferromagnetic quantum phase transition is internally unstable and turns into a first order transition.