Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

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