Migdal-Eliashberg theory breaks down to polaron/bipolaron states before phonon softening at extreme densities, with variational upper bounds on coupling λ showing this occurs well before softening in 2D/3D systems.
For negativek, we verified that (G e(kω0))−1 does not vanish, i.e., there are no poles at negativeω
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Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons
Migdal-Eliashberg theory breaks down to polaron/bipolaron states before phonon softening at extreme densities, with variational upper bounds on coupling λ showing this occurs well before softening in 2D/3D systems.