Sensitivity of non-Hermitian systems

Abstract

Understanding the extreme sensitivity of the eigenvalues of non-Hermitian Hamiltonians to the boundary conditions is of great importance when analyzing non-Hermitian systems, as it appears generically and is intimately connected to the skin effect and the breakdown of the conventional bulk boundary correspondence. Here we describe a method to find the eigenvalues of one-dimensional one-band models with arbitrary boundary conditions. We use this method on several systems to find analytical expressions for the eigenvalues, which give us conditions on the parameter values in the system for when we can expect the spectrum to be insensitive to a change in boundary conditions. By stacking one-dimensional chains, we use the derived results to find corresponding conditions for insensitivity for some two-dimensional systems with periodic boundary conditions in one direction. This would be hard by using other methods to detect skin effect, such as the winding of the determinant of the Bloch Hamiltonian. Finally, we use these results to make predictions about the (dis)appearance of the skin effect in purely two-dimensional systems with open boundary conditions in both directions.

25 pages, 14 figures; v2: title change (previous title was `Stability of non-Hermitian systems') and some minor changes

References in corpus (9)

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• Efficient Light Funneling based on the non-Hermitian Skin Effect
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Cited by in corpus (27)

• Topological Non-Hermitian skin effect
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Exact analogue of the Hatano-Nelson model in 1D continuous nonreciprocal systems
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Dissipative Boundary State Preparation
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Critical non-Hermitian topology induced quantum sensing
• Non-Hermitian extended midgap states and bound states in the continuum
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Anomalous dynamical response of non-Hermitian topological phases
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Topologically compatible non-Hermitian skin effect
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• From Hermitian critical to non-Hermitian point-gapped phases
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Robustness of tripartite entangled states in passive PT-symmetric qubits
• Reversing non-Hermitian skin accumulation with a non-local transverse switch
• Boundary critical phenomena in the quantum Ashkin-Teller model
• Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model
• Enhancement of quantum sensing in a dissipatively coupled two-mode system