Abstract
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with -fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal Stiefel bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this holonomy captures the inherent geometric feature of the state evolution that may not be cyclic. Moreover, a rigorous theory of geometric phase in the evolution of the eigenspace of an adiabatic action operator is also formulated, with the corresponding holonomy being elaborated by a pullback bundle.
- Received 28 February 2005
DOI:https://doi.org/10.1103/PhysRevLett.95.050406
©2005 American Physical Society