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Employing a largely unbiased variational exact diagonalization technique, weanalyze the consequences of longer-ranged electron hopping and electron-phononinteraction on polaron formation in one dimension. Having at our disposal theaccurate ground state energy and wavefunction, we calculate and discuss variousphysical quantities, such as the renormalized band structure, effective mass,wave-function renormalization factor, phonon dressing and Drude weight,characterizing the properties of the polaronic quasiparticle. We demonstratethat the electron-phonon coupling affects the relative strength of thenearest-neigbor (NN) and next-nearest-neigbor (NNN) hopping processes in adynamic way. Most notably we observe that the minimum of the polaron band,occurring at a finite momentum for large negative ratio between NN and NNNtransfer, jumps to zero momentum as the electron-phonon coupling exceeds acritical one, thereby causing a rather sharp polaron transition in theone-dimensional extended Holstein model. The signatures of this transition areseen in the effective mass and polaron mobility, and therefore should be easilydetectable by transport measurements.

Particularities of polaron formation in the extended Holstein model with next nearest neighbor transfer