We study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical behavior can be computed exactly, and we explicitly derive the scaling laws of various observables. While the order-parameter correlation function at criticality satisfies the usual power law with anomalous exponent ${\eta }_{\varphi }=2$, the correlation length and the expectation value of the order parameter exhibit essential singularities upon approaching the quantum critical point from the insulating side, akin to the Berezinskii-Kosterlitz-Thouless transition. The susceptibility, on the other hand, has a power-law divergence with non-mean-field exponent $\gamma =2$. On the semimetallic side, the correlation length remains infinite, leading to an emergent scale invariance throughout this phase.

• Received 4 February 2020
• Accepted 3 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.081112