The large polaron in a magnetic field: Possible existence of a phase transition

It is shown that the ground state energy of a polaron in a magnetic field (calculated in the Feynman approximation) exhibits a discontinuity in the first derivative with respect to α (the electron-phonon coupling constant) if ω_c/ω_o (cyclotron frequency to LO-phonon frequency) is larger than 2.24. This discontinuity has the characteristics of a first order phase transition if α is interpreted as an inverse temperature. For ω_c/ω_o = 2.24 the transition is second order. We found that below the transition point the phonon cloud cannot follow the electron in its motion in the magnetic field.