Title of the Thesis:

“Diagrammatic Monte Carlo and Numerical X-Propagator
methods for polarons with nonlinear electron-phonon interaction”

Defense committee:

Darko Tanasković, University of Belgrade, RS (reviewer)
Chao Zhang, Anhui Normal University, CN (reviewer)
Cesare Franchini (supervisor)
Thomas Pichler (chair)

Abstract

The Holstein Hamiltonian is the prototypical model used to describe small polarons,
quasi-particles arising from the interaction between electron and phonons. In its
conventional form, the Holstein Hamiltonian assumes harmonic phonons and linear
coupling. However, this simplification is inadequate for materials such as hydrides,
quantum paraelectrics, and halide perovskites, where anharmonic effects significantly influence electron-phonon dynamics. This thesis addresses this gap by investigating extensions of the Holstein model featuring "quadratic" and "double-well" electron-phonon coupling. These quantum Hamiltonians are solved by approximation-free, continuous time Monte Carlo methods based on (i) the momentum-space diagrammatic expansion in Feynman diagrams (DiagMC) and (ii) the lattice path integral representation for the electron, dressed by phonon propagators in the displacement basis (XMC). We introduce the Numerical X-Propagator approach, which extends XMC by incorporating a general, tabulated propagator to accurately handle arbitrary degrees of anharmonicity. The results yield new insights into the role of anharmonicity in polaron behavior, advancing theoretical understanding and introducing methodological innovations that enhance the accuracy and applicability of quantum Monte Carlo simulations, while also guiding future experimental exploration in complex materials.