  We study the geometric curvature and phase of the Rabi model. Under the
rotating-wave approximation (RWA), we apply the gauge independent Berry
curvature over a surface integral to calculate the Berry phase of the
eigenstates for both single and two-qubit systems, which is found to be
identical with the system of spin-1/2 particle in a magnetic field. We extend
the idea to define a vacuum-induced geometric curvature when the system starts
from an initial state with pure vacuum bosonic field. The induced geometric
phase is related to the average photon number in a period which is possible to
measure in the qubit-cavity system. We also calculate the geometric phase
beyond the RWA and find an anomalous sudden change, which implies the breakdown
of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution
are ill-defined near the anti-crossing point in the spectrum.
