We report a breakthrough development allowing one to solve a broad class of polaron problems with highly nonlinear electron-phonon coupling that were considered unsolvable without uncontrolled simplifications in the past using a Monte Carlo technique formulated in the coordinate representation for both the particle and the atomic displacements. The only condition is the sign positivity of the hopping amplitude. The technique dramatically simplifies (with the corresponding efficiency gains) for models with dispersionless phonons. Our study sheds important light on the nature and universality of the most striking qualitative and quantitative effects demonstrated by the “standard” (Peierls/Su-Schrieffer-Heeger) model based on the linearized displacement-modulated hopping.

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• Electron-phonon coupling
• Phonons
• Polarons