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Designing non-Hermitian real spectra through electrostatics.

Russell Yang1, Jun Wei Tan2, Tommy Tai3

  • 1Department of Physics, National University of Singapore, Singapore 117551, Singapore; Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK.

Science Bulletin
|December 22, 2022
PubMed
Summary

Researchers developed a new method to design stable non-Hermitian systems using an electrostatics analogy. This approach enables the creation of Hamiltonians with desired real spectra and state localization, overcoming limitations of previous methods.

Keywords:
Band structure engineeringBulk-boundary correspondenceElectrostaticsNon-HermitianNon-Hermitian skin effectReal spectrum

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Area of Science:

  • Quantum physics
  • Non-Hermitian systems
  • Mathematical physics

Background:

  • Non-Hermitian systems offer new physics and applications like lasing and sensing.
  • Stability in non-Hermitian systems requires real eigenenergies, often achieved via parity-time (PT) symmetry.
  • Existing methods for designing stable non-Hermitian systems are limited.

Purpose of the Study:

  • To develop a versatile approach for designing new classes of parent Hamiltonians with real spectra.
  • To exploit a dynamical mechanism for enforcing real spectra.
  • To enable reverse-engineering of Hamiltonians with specific spectral properties.

Main Methods:

  • Utilizing a novel electrostatics analogy for modified non-Hermitian bulk-boundary correspondence.
  • Mapping electrostatic charge to density of states and electric fields to complex spectral flow.
  • Recasting Hamiltonian diagonalization as a Poisson boundary value problem.

Main Results:

  • A comprehensive design approach for parent Hamiltonians with real spectra.
  • Ability to reverse-engineer Hamiltonians with desired spectra and state localization profiles, independent of symmetry principles.
  • Overcoming numerical errors in traditional methods, allowing for larger system sizes.

Conclusions:

  • The electrostatics analogy provides a powerful tool for designing stable non-Hermitian systems.
  • This method expands the possibilities for creating novel Hamiltonians without relying on symmetry.
  • The approach enhances numerical stability and scalability for studying non-Hermitian physics.