  We investigate the geometric phase of a two-level atom (qubit) coupled to a
bosonic reservoir with Lorentzian spectral density, and find that for the
non-Markovian dynamics in which rotating-wave approximation (RWA) is performed,
geometric phase has a $\pi$-phase jump at the nodal point. However, the exact
result without RWA given by hierarchy equation of motion method shows that
there is no such a phase jump or nodal structure in geometric phase. Thus our
results demonstrate that the counter-rotating terms significantly contribute to
the geometric phase in multi-mode Hamiltonian under certain circumstances.
