Effect of electron-phonon interaction range on lattice polaron dynamics: A continuous-time quantum Monte Carlo study

We present the numerically exact ground-state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a continuous-time quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling $1∕\ensuremath{\lambda}$ expansion. We show that the exact results agree well with the canonical Fr\"ohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.

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