Impurity induced non-unitary criticality

In the non-Hermitian SSH model at criticality, the coalesces of the exceptional point implies a $c = -2$ entanglement scaling. In this work, we also obtain similar entanglement scaling by simply adding a local PT-symmetric non-Hermitian impurity on the $c = 1$ critical SSH chain under the periodic boundary condition. In addition, we also discuss the many-body ground state energy scaling and many-body fidelity susceptibility, which remarks an identical CFT structure to the non-Hermitian SSH chain and the novel flow from $c = -2$ to $c = 1$ criticality. Moreover, we also discuss boundary effects and observe that such phenomenon is highly-sensitive to boundary.