Geometric phase in eigenspace evolution of invariant and adiabatic action operators

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with N-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal Stiefel U(N) bundle over a Grassmann manifold. Most significantly, for an...

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Bibliographic Details
Published inPhysical review letters Vol. 95; no. 5; p. 050406
Main Authors Teo, Jeffrey C Y, Wang, Z D
Format Journal Article
LanguageEnglish
Published United States 29.07.2005
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Summary:The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with N-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal Stiefel U(N) 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 U(N) bundle.
ISSN:0031-9007
DOI:10.1103/physrevlett.95.050406