Green's function theory of the large polaron for strong interactions

Leo P. Kadanoff, M. Revzen

Kwangyl Park, Sul-Ah Ahn, Sung‐Ho Suck Salk

Applying the functional Schrodinger picture to the Holstein-Primakoff boson theory, we obtain a dispersion energy relation for an antiferromagnetic spin polaron or magnon in two-dimensional systems of strongly correlated electrons. We show that our magnon ground-state wave function is equivalent to that of a retraceable path approximation by Reiter in the long-wavelength limit. Further, we demonstrate that the derived dispersion relation of a quasiparticle leads to the self-consistent Born approximation of the Green's function approach only in the large Heisenberg coupling J limit, showing that this new approach is general enough to contain more physical information than the Green's function approach in dealing with the antiferroinagnetic spin polaron of interest.

J. T. Devreese, R. P. Evrakd

Nikolay N. Bogolubov, Nikolay N. Bogolubov

D. Matz, B.C. Burkey

A Green's-function equation-of-motion analysis of the large polaron is presented. Existing theories for the ground-state energy and effective mass are obtained from a nondiagonal form of the Fock approximation to the electron self-energy. A connection between the usual canonical transformation techniques and the Green's-function approach is given explicitly. The effects of vertex corrections and translational invariance are examined in the context of these results.

M. Porsch

Abstract A general method for studying the properties of free and bound polarons at arbitrary strength of electron‐phonon coupling is given from a unified point of view by first performing a suitable canonical transformation of the electron and phonon field operators and subsequently applying the double‐time Green's function formalism to the transformed polaron‐phonon Hamiltonian. Calculating the one‐polaron Green's function in the lowest approximation and employing the variational principle for the free energy, a pair of coupled differential equations is derived for the effective wave function and a trial function as introduced by the canonical transformation. From these equations, the weakly excited polaron energy levels at low temperatures can be found in the entire range of coupling constants when external fields are present. In this paper, detailed calculations are confined to the optical‐polaron problem in the zero‐field case. Intermediate‐ and strong‐coupling formulas for temperature‐dependent polaron self‐energy and effective mass are given. The strong‐coupling regime appears to increase with temperature.