Abstract
By varying within a manifold the positive (negaive)-energy eigenvectors of the Hamiltonian (where are the Pauli matrices) form a U(1) fiber bundle. For certain the bundle has nontrivial topology. For example, when the associated bundle has nonzero Chern number indicating that it is topologically nontrivial at the highest level. In this paper we construct a simple Hamiltonian whose eigenvector bundle exhibits a more subtle topological nontriviality when is a closed three manifold. This nontrivial topology is characterized by nonzero Chern-Simons invariant.
- Received 18 April 2001
DOI:https://doi.org/10.1103/PhysRevA.64.052101
©2001 American Physical Society