Polarons with arbitrary nonlinear electron-phonon interaction

TL;DR

This paper introduces an exact computational method for solving complex polaron models with arbitrary nonlinear electron-phonon interactions, enabling analysis of previously intractable systems and revealing diverse regimes of polaron behavior.

Contribution

Develops a novel, exact numerical approach for polaron models with nonlinear couplings, applicable to a wide range of materials and regimes, including those difficult for existing methods.

Findings

Identification of three distinct regimes of polaron behavior.

Exponential scaling of quasiparticle properties in intermediate coupling.

Observation of strong-coupling asymptotic behavior.

Abstract

We develop an exact computational method based on numerical X-propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach covers various polaron models, some of which were impossible to treat by any existing approximation-free techniques. Moreover, it remains efficient in the most relevant but computationally challenging regime of phonon frequencies much smaller than the electron bandwidth. As a case study, we consider the double-well type nonlinear model with quadratic ($g_2<0$) and quartic ($g_4>0$) interactions describing a broad class of technologically important materials, such as quantum paraelectric compounds and halide perovskites. We observe, depending on the model parameters, three qualitatively different regimes: (i) quantum interplay of quartic and quadratic interactions which suppresses effects of the quadratic coupling, (ii) intermediate-coupling regime with exponential $\propto \exp(\alpha g_2 \Omega^{-1/4})$ scaling of the quasiparticle weight and mass renormalization, and (iii) strong-coupling asymptotic behavior.