Reply to "On the cutoff parameter in the translation-invariant theory of the strong coupling polaron"

TL;DR

This paper refutes a previous claim about the polaron ground state energy by showing that their variational functional was incomplete, thus invalidating their conclusions about energy bounds.

Contribution

It demonstrates that the variational functional used in the referenced work is incomplete, challenging prior claims about energy bounds in the strong coupling polaron theory.

Findings

The variational functional in Ref. [1] is incomplete.

The previous argument does not establish an upper bound for the polaron energy.

The same issue applies to bipolaron energy estimates.

Abstract

The present work is a reply to the paper [1]. It is proven that the argumentation of Ref. [1] is inconsistent. The variational functional for the polaron ground state energy considered in Ref. [1] contains an incomplete recoil energy. Since the variational functional of Ref. [1] is incomplete, it is not proven to provide a variational upper bound for the polaron ground-state energy. The same conclusion follows also for the bipolaron ground-state energy.