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.
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3 Pith papers cite this work. Polarity classification is still indexing.
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In the Holstein model, polaronic and bipolaronic states emerge before phonon softening across wide fillings in 2D and 3D, via an intermediate pseudogap mixed state where Luttinger theorem is broken.