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

TL;DR

This study uses a new continuous-time Quantum Monte Carlo method to analyze how the range of electron-phonon interactions influences lattice polaron properties, revealing that longer-range interactions reduce effective mass and affect polaron dynamics.

Contribution

It introduces a numerically exact QMC technique applicable to any interaction range, enabling comprehensive analysis of polaron properties across coupling strengths and adiabatic ratios.

Findings

Longer interaction range reduces polaron effective mass.

Results align with weak and strong coupling theories.

Polaron dynamics are strongly dependent on interaction range.

Abstract

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 new 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 $1/\lambda$ 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.