A note on topological insulator phase in non-hermitian quantum systems

Abstract

Examples of non-hermitian quantum systems admitting topological insulator phase are presented in one, two and three space dimensions. All of these non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained with the introduction of appropriate inner-products in the corresponding Hilbert spaces. The topological invariant characterizing a particular phase is shown to be identical for a non-hermitian Hamiltonian and its hermitian counterpart, to which it is related through a non-unitary similarity transformation. A classification scheme for topological insulator phases in pseudo-hermitian quantum systems is suggested.

Latex, 12 pages, no figure; Added discussions, Version to appear in Journal of Physics: Condensed Matter

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• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
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