The geometric phases γ − ( t ) for instantaneous eigenstate | φ − 〉 under different driving parameters. The thick black solid lines are the analytical solutions of Eq. (58), the thin blue lines are the real phases calculated by Eqs. (54) and (55), the black dotted diagonal lines are the first term of Eq. (58) and the horizonal lines are labeled by Eq. (59) in different driving periods. Insets: the parametric paths of three different driving schemes in the Bloch space, and all the driving paths are counterclockwise. The driving parameters are ω = 0.02 ω 0 , (a) α 0 = 0.2 , α 1 = 0 ; (b) ω / ν = 1 / 2 , α 0 = 0.2 , α 1 = 0.2 ; and (c) ω / ν = 2 / 1 , α 0 = 0.2 , α 1 = 0.1 .