Quantum impurities give rise to rich physical phenomena, with some exhibiting critical behavior described by conformal field theories (CFTs) in the low-energy limit. In parallel, party-time ($\mathcal{PT}$) symmetric non-Hermitian systems host exceptional points (EPs) at criticality, leading to exotic features governed by nonunitary CFTs. Here, we establish a connection between non-Hermitian impurities and CFTs by demonstrating that the critical properties of a $(1+1)$-dimensional free-fermion chain with central charge $c=1$ can be drastically altered by the presence of a local non-Hermitian impurity. Through a systematic analysis of entanglement/Rényi entropy, the finite-size scaling of the many-body spectrum, and fidelity susceptibility, we identify that this impurity-induced non-Hermitian criticality is characterized by a nonunitary CFT with central charge $c=-2$. Furthermore, we find that these nonunitary critical properties exhibit strong sensitivity to boundary conditions.

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• Entanglement entropy
• Non-Hermitian systems
• Conformal field theory
• Conformal symmetry
• Single impurity model