Abstract
We study a particular 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
$\eta_= 2$, the correlation length and the vacuum 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. On the semimetallic side, the
correlation length remains infinite, leading to an emergent scale invariance
throughout this phase. The transition may be realized experimentally using
ultracold fermionic atoms on optical kagome or checkerboard lattices.
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