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Journal of Mathematical Physics

Berry’s phase on SU(n)/S(U(1)×U(n−1)) manifolds

Stefan Giller, Cezary Gonera, Piotr Kosiński, Paweł Maślanka

Published Feb 1, 1996• 1 citation
Publisher

Abstract

It is shown that the Berry phase/matrix for Hamiltonians parametrized by the points of M≡SU(n)/S(U(1)×U(n−1)) and having no accidental degeneracy is expressible in terms of Riemannian connection on M and representations of S(U(1)×U(n−1)).
DOI
10.1063/1.531801

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The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\\"ahler manifold its fundamental K\\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.
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