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General PT-Symmetric Matrices
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Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P'-pseudo-Hermitian with respect to some P' operators. The relation between corresponding P and P' operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.
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Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems
The topology of certain one-dimensional non-Hermitian chains is captured by a Chern number of an effective two-dimensional Hermitian Hamiltonian, and this hidden Chern number predicts zero-real-energy end states.
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