The Eotimes e Jahn-Teller Polaron in Comparison with the Holstein Polaron

Based on an exact expression for the self-energy of the Jahn-Teller polaron, we find that symmetry of pseudospin rotation makes the vertex correction much less effective than that for the Holstein polaron. This ineffectiveness brings about a smaller effective mass m^* and a quantitatively differenent large-to-small polaron crossover, as examined by exact diagonalization in a two-site system. In the strong-coupling and antiadiabatic region, a rigorous analytic expression is found for m^*.