Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

TL;DR

This paper uncovers how the non-Hermitian skin effect induces a nonequilibrium quantum phase transition affecting entanglement dynamics, leading to area-law entanglement entropy and critical phenomena in open quantum systems.

Contribution

It reveals the role of the skin effect in causing entanglement phase transitions and quantum criticality without disorder or interactions, linking non-Hermitian physics to quantum entanglement.

Findings

Skin effect induces a macroscopic particle flow suppressing entanglement propagation.

An entanglement phase transition occurs due to competition between unitary dynamics and the skin effect.

The transition is characterized by a nonunitary conformal field theory with boundary-sensitive central charge.

Abstract

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.