Elliott H. Lieb, Lawrence E. Thomas
Ground state energy of the strong-coupling polaron
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ABSTRACT. The polaron has been of interest in condensed matter theory and field
theory for about half a century, especially its strong coupling limit.
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, $E_0\sim -C\alpha^2$, 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.