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We use the Density Matrix Renormalization Group method to study aone-dimensional chain with Peierls electron-phonon coupling, which describesthe modulation of the electron hopping by lattice distortions. We demonstratethat this system is stable against phase separation in the dilute densitylimit. We only find phase separation numerically for large couplings for whichthe linear approximation for the electron-phonon coupling becomes invalid; thisbehavior can be stabilized in a narrow sliver of the physical parameter spaceif the dispersion of the phonons is carefully tuned. These results indicatethat in the dilute electron density limit, Peierls bipolaron liquids aregenerically stable, unlike in other models of electron-phonon coupling. We showthat this behavior extends to finite carrier concentrations of up to quarterfilling. This stability of low-density, light-mass bipolaron liquids in thePeierls model opens a path to high-$T_c$ superconductivity based on abipolaronic mechanism, in higher dimensions.

Bipolaron liquids at strong Peierls electron-phonon couplings