Hatano-Nelson model with a periodic potential

Abstract

We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.

7 pages, 10 figures

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Cited by in corpus (9)

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• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Non-Hermitian skin effect beyond the tight-binding models
• Tight-binding lattices with an oscillating imaginary gauge field
• Degeneracies and symmetry breaking in pseudo-Hermitian matrices
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain