We investigate the Holstein model by using the dynamical mean-field theory
combined with the exact diagonalization method. Below a critical temperature
Tcr, a coexistence of the polaronic and the bipolaronic solutions is found for
the same value of the electron-phonon coupling $ in the range gc1(T)<g<gc2(T).
In the coexistence region, the system shows a first order phase transition from
the bipolaronic to the polaronic states as T decreases at T=Tp(<Tcr), where the
double occupancy and the lattice fluctuation together with the anharmonicity of
the effective ion potential change discontinuously without any symmetry
breaking. The obtained bipolaronic transition seems to be consistent with the
rattling transition in the beta-pyrochlore oxide KOs2O6.Comment: 5 pages, 5 figures, J. Phys. Soc. Jpn. 79 (2010) 09370
