• Corpus ID: 92979368

Chiral symmetry in non-Hermitian systems: product rule, Clifford algebra and pseudo-chirality

@article{Rivero2019ChiralSI,
  title={Chiral symmetry in non-Hermitian systems: product rule, Clifford algebra and pseudo-chirality},
  author={Jose D. H. Rivero and Li Ge},
  journal={arXiv: Quantum Physics},
  year={2019}
}

• Jose D. H. Rivero, L. Ge
• Published 6 March 2019
• Mathematics
• arXiv: Quantum Physics

Chiral symmetry provides the symmetry protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and the same anti-commutation relation between the Hamiltonian and a linear chiral operator, i.e., $\{H,\Pi\}=0$, now warrants a symmetric spectrum about the origin of the complex energy plane. Here we show two general approaches to construct chiral symmetry in non-Hermitian systems, with an emphasis on lattices with detuned on-site potentials that can vary in both their real and imaginary parts. One approach relies on the simultaneous satisfaction of both non-Hermitian particle-hole symmetry and non-Hermitian bosonic anti-linear symmetry, while the other utilizes the Clifford algebra satisfied by the Dirac matrices. We also distinguish non-Hermitian chiral symmetry from pseudo-chirality, with the latter defined by $\eta H^T \eta^{-1}=-H$ and belonging to a broadened definition of symmetry that maps between the left and right eigenspaces of a non-Hermitian Hamiltonian.