Abstract The dielectric polaron is treated using the Gross unitary transform and the Matz‐Green's function techniques. A two‐particle Feynman‐like model is introduced to compare these methods with the best Feynman path integral formulation. It is found that the introduction of a second particle in the model problem does not improve on the usual result for a one‐particle model. However, a comparison of these different approaches leads to the conclusion that no vertex contributions are contained in the Feynman approximation. It is also concluded that it is the very special treatment of the kinetic energy of the electron in Feynman's theory that makes his results lower in energy.Abstract The dielectric polaron is treated using the Gross unitary transform and the Matz‐Green's function techniques. A two‐particle Feynman‐like model is introduced to compare these methods with the best Feynman path integral formulation. It is found that the introduction of a second particle in the model problem does not improve on the usual result for a one‐particle model. However, a comparison of these different approaches leads to the conclusion that no vertex contributions are contained in the Feynman approximation. It is also concluded that it is the very special treatment of the kinetic energy of the electron in Feynman's theory that makes his results lower in energy.

physica status solidi (b)Jan 1, 19811 citation

The Green's Function of the 1D Breathing-Mode Polaron

Glen L. Goodvin, Mona Berciu

Bulletin of the American Physical SocietyMar 10, 20080 citations

Hamiltonian approach to Feynman's path-integral polaron treatment

J. T. Devreese, Serghei N. Klimin

Bulletin of the American Physical SocietyMar 22, 20110 citations

Polaron Problem by Diagrammatic Quantum Monte Carlo

Nikolay V. Prokof'ev, Boris V. Svistunov

We present a numerical solution of the polaron problem by a novel Monte Carlo method. Starting from a conventional diagrammatic expansion for the polaron Green function $G(\mathbf{k},\ensuremath{\tau})$, we construct a process which generates continuous random variables $\mathbf{k}$ and $\ensuremath{\tau}$, with a distribution function coinciding exactly with $G(\mathbf{k},\ensuremath{\tau})$. The polaron spectrum is extracted from the asymptotic behavior of the Green function. We compare our results for the polaron energy with the variational treatment of Feynman, and present an accurate dispersion curve which features an end point at finite momentum.We present a numerical solution of the polaron problem by a novel Monte Carlo method. Starting from a conventional diagrammatic expansion for the polaron Green function $G(\mathbf{k},\ensuremath{\tau})$, we construct a process which generates continuous random variables $\mathbf{k}$ and $\ensuremath{\tau}$, with a distribution function coinciding exactly with $G(\mathbf{k},\ensuremath{\tau})$. The polaron spectrum is extracted from the asymptotic behavior of the Green function. We compare our results for the polaron energy with the variational treatment of Feynman, and present an accurate dispersion curve which features an end point at finite momentum.

arXiv:cond-mat/9804097Physical Review LettersSep 21, 1998331 citations

\mathbf{k}

and $\ensuremath{\tau}$, with a distribution function coinciding exactly with $G(\mathbf{k},\ensuremath{\tau})$. The polaron spectrum is extracted from the asymptotic behavior of the Green function. We compare our results for the polaron energy with the variational treatment of Feynman, and present an accurate dispersion curve which features an end point at finite momentum.