  Recent years have seen remarkable development in open quantum systems
effectively described by non-Hermitian Hamiltonians. A unique feature of
non-Hermitian topological systems is the skin effect, anomalous localization of
an extensive number of eigenstates driven by nonreciprocal dissipation. Despite
its significance for non-Hermitian topological phases, the relevance of the
skin effect to quantum entanglement and critical phenomena has remained
unclear. Here, we find that the skin effect induces a nonequilibrium quantum
phase transition in the entanglement dynamics. We show that the skin effect
gives rise to a macroscopic flow of particles and suppresses the entanglement
propagation and thermalization, leading to the area law of the entanglement
entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement
phase transition induced by the competition between the unitary dynamics and
the skin effect even without disorder or interactions. This entanglement phase
transition accompanies nonequilibrium quantum criticality characterized by a
nonunitary conformal field theory whose effective central charge is extremely
sensitive to the boundary conditions. We also demonstrate that it originates
from an exceptional point of the non-Hermitian Hamiltonian and the concomitant
scale invariance of the skin modes localized according to the power law.
Furthermore, we show that the skin effect leads to the purification and the
reduction of von Neumann entropy even in Markovian open quantum systems
described by the Lindblad master equation. Our work opens a way to control the
entanglement growth and establishes a fundamental understanding of phase
transitions and critical phenomena in open quantum systems far from thermal
equilibrium.
