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Non-Hermitian systems can now exhibit diabolic points, crucial for topological transitions, thanks to new symmetries enabling real eigenvalues and orthogonal eigenstates. This breakthrough bridges non-Hermitian physics with phenomena like topological phase transitions and Landau levels.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Topological physics

Background:

  • Non-Hermitian systems with gain/loss typically feature exceptional points, not diabolic points.
  • Diabolic points are essential for topological transitions in Hermitian systems.
  • Parity-time symmetric Hamiltonians yield real spectra but nonorthogonal eigenstates, hindering diabolic point formation.

Purpose of the Study:

  • To introduce a novel symmetry framework for non-Hermitian systems.
  • To enable the emergence of diabolic points in non-Hermitian systems.
  • To explore phenomena previously exclusive to Hermitian systems within a non-Hermitian context.

Main Methods:

  • Introduction of a specific pair of symmetries.
  • Demonstration of induced real eigenvalues and pairwise eigenstate orthogonality.
  • Construction of non-Hermitian models exhibiting key phenomena.

Main Results:

  • The proposed symmetries allow non-Hermitian systems to host diabolic points.
  • Exemplary phenomena, including Haldane-type topological phase transitions, magnetic-field-free Landau levels, and Weyl points, are realized in non-Hermitian models.
  • A direct connection is established between non-Hermitian physics and diabolic point phenomenology.

Conclusions:

  • The developed symmetry framework expands the scope of non-Hermitian physics.
  • Non-Hermitian systems can now exhibit a richer topological and quantum mechanical behavior.
  • This work opens new avenues for exploring topological phenomena in dissipative systems.