  We study the Landau-Zener transitions generalized to multistate systems.
Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we
introduce the auxiliary Hamiltonians that are interpreted as the
counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy
the zero curvature condition. The general structures of the auxiliary
Hamiltonians are studied in detail and the time-evolution operator is evaluated
by using a deformation of the integration contour and asymptotic forms of the
auxiliary Hamiltonians. For several spin models with transverse field, we
calculate the transition probability between the initial and final ground
states and find that the method is useful to study nonadiabatic regime.
