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We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for…
We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a…
We present recent advances in understanding of the ground and excited states of the electron-phonon coupled systems obtained by novel methods of Diagrammatic Monte Carlo and Stochastic Optimization, which enable the approximation-free…
We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest…
The ground-state energy, the effective mass and the number of virtual phonons of the optical large polaron confined strictly in one dimension have been estimated by using the generalized Gaussian approximation. The leading-order terms take…
The main quasi-particle characteristics of the one-dimensional polaron are estimated within and beyond the most general Gaussian approximation at arbitrary electron-phonon coupling. We have derived explicitly the ground-state energy and the…
The work is devoted to obtaining the 1D bipolaron functional by Holstein method for the continuum approximation. We analyzed the effect of electron correlations associated with the direct dependence of the wave function of the electron…
A new variational technique is developed to investigate the polaronic features of the Holstein Molecular Crystal Model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown…
We study the crossover from quasi free electron to small polaron in the Holstein model for a single electron by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice. We show that the…
We use both a perturbative Green's function analysis and standard perturbative quantum mechanics to calculate the decrease in energy and the effective mass for an electron interacting with acoustic phonons. The interaction is between the…
We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the…
The polaron features of the one-dimensional Holstein Molecular Crystal Model are investigated by improving a variational method introduced recently and based on a linear superposition of Bloch states that describe large and small polaron…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and…
The Holstein model often serves as an archetype for electron-phonon interactions and polaron formation in solids. However, precise descriptions of the Holstein polaron are difficult when the phonon frequency is small and the electron-phonon…
We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total…
The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Pad\'e rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of…
The polaron energy and the effective mass are calculated for an electron confined in a finite quantum well constructed of $GaAs/Al_x Ga_{1-x} As$ layers. To simplify the study we suggest a model in which parameters of a medium are averaged…
We calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling…
The reconstruction of photon conversions is importantin order to improve the reconstruction efficiency of the physics measurements involving photons. However, there are significant number of conversions in which only one of the two tracks…