On the global minimum of the energy-momentum relation for the polaron

TL;DR

This paper proves that for the Fröhlich large polaron model, the ground state energy reaches its minimum at zero momentum, indicating no localization transition occurs at finite coupling.

Contribution

It establishes the uniqueness of the global minimum of the energy-momentum relation at zero momentum for the Fröhlich polaron, clarifying ground state properties.

Findings

Ground state energy has a unique minimum at zero momentum.

No ground state exists for the Fröhlich Hamiltonian at finite coupling.

Localization transition is excluded at finite coupling.

Abstract

For the Fr\"ohlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the Fr\"ohlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.