  The emergence of the bipolaronic phase and the formation of the
heavy-electron state in the anharmonic Holstein model are investigated using
the dynamical mean-field theory in combination with the exact diagonalization
method. For a weak anharmonicity, it is confirmed that the first-order
polaron-bipolaron transition occurs from the observation of a discontinuity in
the behavior of several physical quantities. When the anharmonicity is
gradually increased, the polaron-bipolaron transition temperature is reduced as
well as the critical values of the electron-phonon coupling constant for
polaron-bipolaron transition. For a strong anharmonicity, the polaron-bipolaron
transition eventually changes to a crossover behavior. The effect of
anharmonicity on the formation of the heavy-electron state near the
polaron-bipolaron transition and the crossover region is discussed in detail.
