I have vague memories of having read somewhere that if you have a parameter manifold that(adsbygoogle = window.adsbygoogle || []).push({});

a) Have a non-trivial Berry phase (meaning the line integral of the berry connection is non zero for some curve)

and

b) the Berry curvature is non-singular anywhere in that manifold

then you can always extend naturally that manifold to bigger one (so the original manifold becomes a submanifold of the new one) where the Berry curvature have singularities and that singularities act as the "source" of the Holonomy.

It is that a fact or I'm misremembering something?

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# Help me check a fact about Berry phase

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