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Polarons with arbitrary nonlinear electron-phonon interaction

Stefano Ragni1, Tomislav Miškić2, Thomas Hahn3, Nikolay Prokof'ev4, Osor S. Barišić2, Naoto Nagaosa5,6, Cesare Franchini1,7,*, and Andrey S. Mishchenko2,5,†

  • *Contact author: cesare.franchini@univie.ac.at
  • †Contact author: andrey.mishchenko6363@gmail.com
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Phys. Rev. Research 7, 043304 – Published 16 December, 2025

DOI: https://doi.org/10.1103/6127-phps

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 (g2<0) and quartic (g4>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: (1) quantum interplay of quartic and quadratic interactions that suppresses effects of the quadratic coupling, (2) intermediate-coupling regime with exponential ∝exp(αg2Ω−1/4) scaling of the quasiparticle weight and mass renormalization, and (3) strong-coupling asymptotic behavior.

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Phys. Rev. Research 7, 043304– Published 16 December, 2025
  • Received 26 June 2025
  • Accepted 12 November 2025
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