Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation

Details Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation

2008-07-22

arxiv.org/abs/0807.3405v2

J. Math. Phys. 49, 082105 (2008)

Physics

Quantum Physics

22 pages, 1 figure, published version

Scientific paper

10.1063/1.2968344

For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and the lines 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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