A single electron in one dimensional lattice is considered within the framework of extended Holstein model at strong-coupling limit. Disordered density-displacement type electron-phonon interaction is proposed. Basic parameters of small polaron formed due to disordered electron-phonon interaction are calculated. It is shown that disordered electron-phonon interaction substantially influences all properties of the polaron. Depending on disordered electron-phonon interaction polaronic effect might be enhanced or diminished. It turns out that all parameters of the polaron are site dependent. Further application of proposed model is briefly discussed.
We study the properties of an impurity immersed in a weakly interacting Bose gas, i.e., of a Bose polaron. In the perturbatively tractable limit of weak impurity-boson interactions many of its properties are known to depend only on the scattering length. Here we demonstrate that for strong (unitary) impurity-boson interactions all quasiparticle properties of a heavy Bose polaron, such as its energy, its residue, its Tan's contact, and the number of bosons trapped nearby the impurity, depend on the impurity-boson potential via a single parameter characterizing its range.
Using the Lanczos method in linear chains we study the double exchange model in the low concentration limit, including an antiferromagnetic super-exchange K. In the strong-coupling limit we find that the ground state contains ferromagnetic polarons whose length is very sensitive to the value of
K/t. We investigate the dispersion relation, the trapping by impurities, and the interaction between these polarons. As the overlap between polarons increases, by decreasing
K/t, the effective interaction between them changes from antiferromagnetic to ferromagnetic. The scaling to the thermodynamic limit suggests an attractive interaction in the strong-coupling regime
(Jh>t) and no binding in the weak limit ${(J}_{h}\ensuremath{\simeq}t).$