In pursuit of deconfined quantum criticality in Ising gauge theory entangled with single-component fermions

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