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arXiv:1208.1166 · Solid State Communications

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

Serghei N. Klimin, J. T. Devreese

Published Oct 16, 2012• 10 citations
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Abstract

The present work is a reply to the paper [1]. It is proven that the argumentation of Refs. [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.

DOI
10.1016/j.ssc.2012.10.012

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The present work is a reply to the paper [1]. It is proven that the argumentation of Refs. [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.
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.
Abstract A general formalism for diagonalizing quadratic forms of boson operators [7], is used to obtain a translationally invariant variational ansatz which is suitable for calculating the polaron self‐energy, effective mass, and energy momentum relation in both coupling limits. The self‐energy and effective mass are calculated in the weak‐coupling limit. The strong coupling limit shows the wellknown α2‐dependence of the self‐energy. Diagonalizing the quadratic part of the recoil term gives rise to an additional self‐energy contribution to the cutoff.
The ground-state characterization of the polaron problem is retrieved within the framework of a variational scheme proposed previously by Devreese et al for the bound polaron. The formulation is based on the standard canonical transformation of the strong coupling ansatz and consists of a variationally determined perturbative extension serving for the theory to interpolate in the overall range of the coupling constant. Specializing our considerations to the bulk and strict two-dimensional polaron models we see that the theory yields significantly improved energy upper bounds in the strong coupling regime and, moreover, extrapolates itself successfully towards the well-established weak coupling limits for all polaron quantities of general interest.