Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation

Abstract

For an arbitrary possibly non-Hermitian matrix Hamiltonian H that might involve exceptional points, we construct an appropriate parameter space M and line bundle Ln over M such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of Ln. We examine the case of 2×2 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. © 2008 American Institute of Physics.