Limits of the non-Hermitian description of decay models

Abstract

We present a general proof that non-Hermitian dynamics and Lindblad dynamics with only decay terms are equivalent in the highest particle subspace. We then propose an unbiased method to determine if a system's dynamics in the highest-particle subspace is non-Hermitian. We exemplify this for a simple two-site decay system connected to two baths, and find that the exact solution is well approximated by non-Hermitian dynamics only in the weak-coupling and in the singular-coupling limits, where a Lindbladian description was already known to be accurate. The fact that an accurate non-Hermitian description is so limited, even for such a simple system, raises doubts about how valid such descriptions are for more complicated systems away from these asymptotic limits. Finally, we prove that for models with a nondegenerate system Hamiltonian, exceptional points cannot occur in the weak-coupling limit. This result is relevant for the design of experiments that aim to identify such exceptional points.

References in corpus (14)

• Topological Origin of Non-Hermitian Skin Effects
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• Topological quantum state control through exceptional-point proximity
• Exceptional points of the Lindblad operator of a two-level system
• Topological input-output theory for directional amplification
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• The operator growth hypothesis in open quantum systems
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Hidden zero modes and topology of multiband non-Hermitian systems
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials

Cited by in corpus (2)

• Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains