Publication:
Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation

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College of Sciences

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Mehri-Dehnavi, Hossein

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For an arbitrary possibly non-Hermitian matrix Hamiltonian H that might involve exceptional points, we construct an appropriate parameter space m and line bundle L-n over m such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of L-n. We examine the case of 2 X 2 matrix Hamiltonians in detail and show that, contrary to claims made in some recent publications, geometric phases arising from encircling exceptional points are generally geometrical and not topological in nature.

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American Institute of Physics (AIP) Publishing

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Mathematics

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Journal of Mathematical Physics

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10.1063/1.2968344

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