Boson-Mediated Electronic Correlations: From Phonons to PhotonsKovač, Klemen (Avtor) Bonča, Janez (Mentor) Golež, Denis (Komentor) boson-mediated electronic correlationselectron-phonon interactionelectron-photon interactionpolaronsbipolaronspreformed pairsnonequilibrium dynamicsphoton-mediated interactionspolaritonsextended dynamical mean-field theoryThis thesis investigates how bosonic environments reshape electronic correlations in quantum many-body systems, with emphasis on two complementary classes of mediators: lattice vibrations and quantized electromagnetic modes. The central question is how such bosonic degrees of freedom renormalize electronic motion, generate effective interactions, and open routes toward controlling correlated states. The first part of the thesis focuses on phonon-mediated correlations in the Holstein–Hubbard model. We study how dispersive optical phonons modify bipolaron binding, mobility, and single-particle spectra. We show that phonon dispersion can substantially reshape both the stability of bound pairs and their spectroscopic fingerprints. We further demonstrate that electron-removal spectra can already contain clear signatures of preformed pairs: a liquid of incoherent bipolarons exhibits a depletion of low-energy spectral weight near the chemical potential while remaining metallic, and its spectra can be understood in terms of a simple Bose-sea picture of hard-core pairs. The second part addresses nonequilibrium control of phonon-mediated interactions. For a system with nonlinear electron–phonon coupling driven by a short optical pulse, numerically exact time evolution reveals that phonon driving can switch the effective electron–electron interaction between attraction and repulsion. In the oscillator-softening regime, the pulse can create a long-lived metastable bound state that persists after the field is turned off, reflecting a configuration-selective redistribution of phonon excitations rather than a purely Floquet mechanism. The final part turns to photon-mediated correlations in structured electromagnetic environments. Within extended dynamical mean-field theory, we study a system in which intrinsic static interactions coexist with retarded photon-mediated couplings. The results reveal a superradiant-like ordered phase driven by the softening of a collective polaritonic mode and show that static interactions can assist the emergence of this order. Taken together, the thesis highlights bosons not only as mediators of correlations, but also can serve as a tool for controlling correlated electronic behavior.20262026-05-29 08:15:05Doktorsko delo/naloga182949VisID: 160367COBISS_ID: 280791299sl