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arXiv · 1810.10729

Non-Hermitian quantum systems and their geometric phases

Qi Zhang·Biao Wu
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Abstract

We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic evolution of non-Hermitian quantum systems. We find that the adiabatic evolution is possible only when the eigen-energies are real. The accompanying geometric phase is found to be generally complex and associated with not only the phase of a wavefunction but also its amplitude. The condition for the real geometric phase is laid out. Our results are illustrated with two examples of non-Hermitian $\mathcal{PT}$ symmetric systems, the two-dimensional non-Hermitian Dirac fermion model and bosonic Bogoliubov quasi-particles.

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Qi Zhang, Biao Wu. 2018-10-25. Non-Hermitian quantum systems and their geometric phases. https://doi.org/10.1103/physreva.99.032121

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