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Since R(t=0) = R(t=T), difference in \phi = 2 pi n, where n is any integers.

As gauge transform would lead to 2 pi n difference, berry phase is determined up to 2pi n.

However, when we calculate berry phase for bloch bands,

it gives 2 pi n, and this is not determined up to 2 pi n (otherwise chern number is always zero).

Would anybody solve my problem? Many thanks