  We highlight exotic quantum criticality of quasi-two-dimensional
single-component fermions at half-filling that are minimally coupled to a
dynamical Ising gauge theory. With the numerical matrix product state based
iDMRG method, we discover a robust quantum critical line in the infinite
cylinder geometry, where gauge confinement and dimerized translation symmetry
breaking emerge simultaneously. We investigate how the transition can be split
by a $\mathbb{Z}_2$ topologically ordered dimerized phase that is stabilized by
additional short-range repulsive interactions. We conjecture a $u(1)$
deconfined criticality scenario, propose a corresponding low-energy effective
field theory of the exotic quantum critical point in the two-dimensional limit
and identify its shortcomings
