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Bulk-Boundary Correspondence and Exceptional Points for a Dimerized Hatano-Nelson Model with Staggered Potentials

by Yasamin Mardani, Rodrigo Alves Pimenta, Jesko Sirker

Submission summary

Authors (as registered SciPost users): Rodrigo A. Pimenta
Submission information
Preprint Link: https://arxiv.org/abs/2410.01542v1  (pdf)
Date submitted: 2024-10-06 09:14
Submitted by: Pimenta, Rodrigo A.
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical

Abstract

It is well-known that the standard bulk-boundary correspondence does not hold for non-Hermitian systems in which also new phenomena such as exceptional points do occur. Here we study by analytical and numerical means a paradigmatic one-dimensional non-Hermitian model with dimerization, asymmetric hopping, and imaginary staggered potentials. We present analytical solutions for the eigenspectrum of this model with both open and closed boundary conditions as well as for the singular-value spectrum. We explicitly demonstrate the proper bulk-boundary correspondence between topological winding numbers in the periodic case and singular values in the open case. We also show that a non-trivial topology leads to protected eigenvalues in the entanglement spectrum. In the $\mathcal{PT}$-symmetric case, we find that the model has a phase where exceptional points become dense in the thermodynamic limit.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing

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