Berlin 2024 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 28: Topology: Other Topics

TT 28.9: Talk

Tuesday, March 19, 2024, 11:45–12:00, H 3025

Analytic approches to non-hermitan systems: Hatano-Nelson model with onsite impurity — •Nico Leumer and Dario Bercioux — DIPC, San Sebastian, Spain

The topology of non-hermitian (nh) systems is undoubtedly a new and interesting field of research. The change from hermitian to non-hermitian Hamiltonian’s demanded the adaptation of former well-established concepts [1]. A striking feature is that nh single band models as the Hatano-Nelson (HN) inherit non-trivial topology.

Since spectra and eigenvectors of nh systems may show numerical instabilities close to so called exceptional points, analytic validation is important. In this perspective, we show that our exact approach using Fibonacci polynomials is also capable of treating generic boundary conditions and arbitrary systems length in the nh case [2, 3]. For the sake of a showcase, we present results for Hatano-Nelson model with periodic and open boundary conditions. For the latter, we include also an impurity at (of) arbitrary position (strength) in order to better illustrate the potential of our technique.

Importantly, the impurity strength influences wavefunction profiles and leads to the formation of linearly decaying modes already for the hermitian case. Interestingly, these specific modes mark a crossover in the energy spectrum where a single mode leaves the band and becomes energetically separated from all remaining ones.

[1] E. J. Bergholtz et al., Rev. Mod. Phys. 93 (2021) 015005

[2] N. Leumer et al., J. Phys.: Condens. Matter 32 (2020) 445502

[3] N. G Leumer, J. Phys. A: Math. Theor. 56 (2023) 435202

Keywords: Hatano-Nelson model with impurity; Non-hermitian Hamiltonian; Exact analytic treatment; Linear decaying modes; Single electron band escape