Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

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, which is the 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.

AdS/BCFT with brane-localized scalar field

“…The above results imply that as the non-unitary effect gets larger, the entanglement growth gets reduced. This is analogous to the measurement-induced phase transition [120][121][122] and the entanglement transition in non-hermitian systems [123]. This suggests that our time-dependent solution with the EOW brane with a ghost field may be a gravity dual of an open quantum system where a quantum system evolves in a non-unitary way derived by e.g.…”

Non-Hermitian topological phases: principles and prospects

“…This approach can provide a theoretical understanding of the various phases and their transitions while uncovering the rich interplay of non-equilibrium many-body physics and topology [67]. As reported in recent studies, entanglement entropy and entanglement dynamics can act as an important diagnostic tools which reveal the topological signatures of a non-Hermitian many-body systems [287][288][289][290].…”

Enhanced entanglement negativity in boundary-driven monitored fermionic chains

“…shown that the entanglement dynamics of monitored free fermions display a subtle behavior, with transitions and crossovers between phases with sub-extensive scaling [30,32,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. This phenomenon was quantitatively understood only very recently, exploiting a mapping to effective non-linear-sigma-model field theories [34,[55][56][57], see also [33].…”