Renormalized energy of ground and first excited state of Fr\"{o}hlich polaron in the range of weak coupling

TL;DR

This paper calculates the renormalized energies of the ground and first excited states of the Fröhlich polaron in the weak coupling regime using diagrammatic summation, revealing how increased coupling affects their spectral positions and stability.

Contribution

It introduces a partial summation technique for the two-phonon mass operator to accurately determine polaron spectral parameters at weak coupling.

Findings

Ground state energy remains stable with increasing coupling.

First excited state shifts to lower energy and decays at higher coupling.

Renormalization effects are significant in weak coupling regime.

Abstract

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant.