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 computational resources (12-digit accuracy for the 1d polaron energy at intermediate coupling). We compute ground and low-lying excited state properties of the model at...

We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism...

Polaron and bipolaron formation in the Holstein-Hubbard model with harmonic confinement potential, relevant to quantum dot structures, is investigated in one to three dimensions by means of unbiased quantum Monte Carlo simulations. The discrete nature of the lattice and quantum phonon effects are fully taken into account. The dependence on phonon frequency, Coulomb repulsion, confinement streng...

There is a growing understanding that transport properties of complex oxides and individual molecules are dominated by polaron physics. In superconducting oxides the long-range Fröhlich and short-range JahnTeller electron-phonon interactions bind carriers into real space pairs small bipolarons with surprisingly low mass but sufficient binding energy, while the long-range Coulomb repulsion keeps...

We investigate the attractive Fermi polaron problem in two dimensions using nonperturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calcul...

We consider the effects of impurities on polarons in three-dimensions (3D) using a continuous time quantum Monte-Carlo algorithm. An exact treatment of the phonon degrees of freedom leads to a very efficient algorithm and we are able to compute the polaron dynamics on an infinite lattice by developing an auxiliary weighting scheme. The magnitude of the impurity potential, the electronphonon cou...

The interaction of a free electron with a polar lattice possessing more than one infrared-active opticalphonon mode is considered. From the full Lagrangian describing the electron-lattice system in the presence of an applied field we derive an effective electron-phonon coupling constant and an effective longitudinal opticalphonon frequency that we argue give accurate predictions when used in th...

We present selected results for the Holstein molecular crystal model in one space dimension as determined by the Global-Local variational method, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparable results of numerous other methodologies of current interest, including quantumMonte Carlo, cluster diagonalization,...

We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism...

To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variational Lang-Firsov transformation, combined with a perturbative calculation of the electron-phonon self-energy in the framework of generalized Matsuba...