Feynman's path-integral polaron treatment approached using time-ordered operator calculus

TL;DR

This paper reformulates Feynman's polaron approach using time-ordered operator calculus, explicitly deriving excited state energies and lifetimes, and validating results against quantum Monte Carlo data.

Contribution

It introduces a Hamiltonian formalism with time-ordered operators to extend Feynman's polaron approach, including excited states and their properties.

Findings

Explicit excited state energies and lifetimes derived

Strong agreement with quantum Monte Carlo optical conductivity peaks

First-time derivation within all-coupling approach

Abstract

The Feynman all-coupling variational approach for the polaron is re-formulated and extended using the Hamiltonian formalism with time-ordered operator calculus. Special attention is devoted to the excited polaron states. The energy levels and the inverse lifetimes of the excited polaron states are, for the first time, explicitly derived within this all-coupling approach. Remarkable agreement of the obtained transition energies with the peak positions of the polaron optical conductivity calculated using diagrammatic quantum Monte Carlo is obtained.