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First Order Bipolaronic Transition at Finite Temperature in the Holstein Model

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.