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We present a comparative analysis of the validity of Eliashberg theory for the cases of fermions interacting with an Einstein phonon and with soft nematic fluctuations near an Ising-nematic/Ising-ferromagnetic quantum-critical point (QCP).…
The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study…
We study polarons in the one-dimensional Bond-Peierls electron-phonon model, in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites, and contrast the results to those known for the Breathing-Mode…
The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on…
Electron-electron and electron-phonon interactions are responsible for the formation of spin, charge, and superconducting correlations in layered quantum materials. A paradigmatic model for such materials that captures both kinds of…
The Hubbard-Holstein model is a simple model including both electron-phonon interaction and electron-electron correlations. We review a body of theoretical work investigating the effects of strong correlations on the electron-phonon…
We study the lattice dynamics of iron superconductor FeSe, and address the fundamental question of how important is proper description of fluctuating magnetic moments in metallic systems for phonon dispersion and phonon density of states.…
With the objective of simulating the physical behavior of electrons in a dynamic background, we investigate a cold atomic Bose-Fermi mixture confined in an optical lattice potential solely affecting the bosons. The bosons, residing in the…
Looking for superconductors with higher transition temperature requires a guiding principle. In conventional superconductors, electrons pair up into Cooper pairs via the retarded attraction mediated by electron-phonon coupling.…
An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ($e$-ph) interactions in quantum materials. Despite the growing importance of this area of research, the community…
We characterize the response of a Mott insulating system to a static electric field in terms of its conducting and spectral properties. Dissipation is included by a coupling to fermionic baths and to either optical or acoustic phonons. This…
Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state…
We study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing…
To reduce the rapidly growing computational cost of the dual fermion lattice calculation with increasing system size, we introduce two embedding schemes. One is the real fermion embedding, and the other is the dual fermion embedding. Our…
We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a…
We extend a recently introduced semiclassical approach to calculating the influence of local lattice fluctuations on electronic properties of metals and metallic molecular crystals. The effective action of electrons in degenerate orbital…
We have studied the interplay of a local phonon mode embedded in a metallic host (Holstein impurity model) using Abelian bosonization. The phonon frequency softens, which takes place in two steps: first, their frequency starts softening,…
We use a Luttinger-Ward functional approach to study the problem of phonon-mediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams…
Positional polymorphism in solids refers to locally disordered unit cells that, on average, reproduce the high-symmetry structures observed in diffraction experiments. Standard theories of electron-phonon interactions fail to describe the…
Electron-phonon coupling, diagonal in a real space formulation, leads to polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if non-diagonal pairing is involved into…