Liouvillian Skin Effect in an Exactly Solvable Model

Yang, Fan; Jiang, Qing-Dong; Bergholtz, Emil J.

doi:10.48550/arxiv.2203.01333

Cited by 1 publication

(3 citation statements)

References 64 publications

(131 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the Liouvillian L is not an operator but a superoperator, it is still non-Hermitian. Consequently, L can exhibit the skin effect in a similar manner to non-Hermitian Hamiltonians [129][130][131][132][133]. Here, we demonstrate that the Liouvillian skin effect has a significant influence on the open quantum dynamics described by the master equation.…”

Section: Purification Induced By the Liouvillian Skin Effectmentioning

confidence: 59%

“…This contrasts with the Liouvillians in Refs. [129,131,133], in which the total particle number decreases with time.…”

Section: L=1mentioning

confidence: 99%

“…In these experiments, reciprocity-breaking dissipation is introduced by the asymmetry of the hopping amplitudes. It is also relevant to Liouvillians for a quantum master equation [129][130][131][132][133]. The skin effect may open up a way to actively control the phases of matter.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

Kawabata¹,

Numasawa²,

Ryu³

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract