Complex Wannier centers derived from nonunitary Wilson loops in non-Hermitian Hamiltonians predict directional drift of Wannier functions and a bulk-boundary correspondence for filling anomalies and gain/loss in edge modes.
Mostafazadeh,PseudoHermiticity versus PT symmetry 2
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abstract
We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.
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Complex Wannier centers and drifting Wannier functions in non-Hermitian Hamiltonians
Complex Wannier centers derived from nonunitary Wilson loops in non-Hermitian Hamiltonians predict directional drift of Wannier functions and a bulk-boundary correspondence for filling anomalies and gain/loss in edge modes.
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Mobility edges in pseudo-unitary quasiperiodic quantum walks
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
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Atiyah--Singer Index Theorem for Non-Hermitian Dirac Operators
The index of non-Hermitian Dirac operators that anticommute with a chirality operator is topologically protected when the operators are diagonalizable and elliptic.
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Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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