Non-unitary dynamics of 2+1d free Fermions: Emergent quantum criticality

We investigate non-unitary random dynamics of 2+1d free Fermion models. Compared to unitary dynamics where the system is evolved towards equilibration with a volume-law entanglement, the additional imaginary non-unitary dynamics leads to a dynamical steady state that displays a unique entanglement scaling behavior similar to that of a Fermi liquid ground state. Besides, both the mutual information and squared two-point correlation function of the steady state exhibit a typical power-law scaling. Thus, our results demonstrate a novel approach towards quantum criticality via a specified non-unitary random dynamics.