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Applying the canonical transformation with the 1/\lambda perturbationexpansion in the nonadiabatic and intermediate regime and the discretegeneralisation of Pekar's continuous nonlinear equation in the extremeadiabatic regime we show that there are no strings in narrow-band ionicinsulators due to the Frohlich electron-phonon interaction alone. Themulti-polaron system is a homogeneous state in a wide range of physicallyinteresting parameters, no matter how strong correlations are. At the same timethe Frohlich interaction allows the antiferromagnetic interactions and/or ashort-range electron-phonon interactions to form short strings in dopedantiferromagnetic insulators if the static dielectric constant is large enough.Comment: 4 pages 1 postscript figur

Strings in charge-transfer Mott insulators: Effects of lattice vibrations and the Coulomb interaction