Exact Ground State Energy of the Strong-Coupling Polaron

The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant, α. It was not until 1983, however, that a proof of the asymptotic formula for the ground state energy was finally given by using difficult arguments involving the large deviation theory of path integrals. Here we derive the same asymptotic result, E0 ∼ −Cα 2, and with explicit error bounds, by simple, rigorous methods applied directly to the Hamiltonian. Our method is easily generalizable to other settings, e.g., the excitonic and magnetic polarons. The polaron Hamiltonian of Fröhlich [1] is a model for the Coulomb interaction of one or more electrons with the quantized phonons of an ionic crystal. In the course of time it was also seen to be an interesting field theory model of non-relativistic particles interacting with a scalar boson field, and it was widely studied [2, 3, 4, 5, 6, 7, 8, 9] in both contexts. c ©1996 by the authors. Reproduction of this article, by any means, is permitted for non-commercial purposes.