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.
To do this, we evalu- ate the off-diagonal elements of the dressed hopping op- erator ˜V= P i,j tijc† i cjX † i Xj
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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.