Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect

Abstract

We show for generic quantum non-Hermitian tight-binding models that relaxation timescales of local observables are not controlled by the localization length ${\xi }_{\mathrm{loc}}$ associated with the non-Hermitian skin effect, contrary to popular belief. Instead, interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation; this is ultimately a consequence of causality and locality. Focusing on the paradigmatic Hatano-Nelson model, we demonstrate that there exists instead a much larger length scale ${\xi }_{\mathrm{prop}}$ which controls the rate of decay towards the steady state. Further, varying ${\xi }_{\mathrm{prop}}$ can lead to anomalously large relaxation times that scale with system size, or to the expected behavior where the dissipative gap correctly predicts the rate of decay. Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.

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Cited by in corpus (20)

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• Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
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• Non-Markovian skin effect
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
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• Lindbladian versus Postselected Non-Hermitian Topology
• Manipulating the Relaxation Time of Boundary-Dissipative Systems through Bond Dissipation
• Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Boom and bust cycles due to pseudospectra of matrices with unimodular spectra