The ground-state energy of a two-level tunnelling unit in a phonon field

Abstract

The ground-state energy of a truncated two-level localised tunnelling system coupled to a phonon field is studied within the framework of small-polaron theory by a variational calculation. In former similar calculations, even when treating the intermediate-coupling region and with finite-polaron bandwidth, a very large coupling-strength parameter was tacitly assumed in the variational procedure, while the ratio of the rigid-lattice tunnelling matrix element to the small-polaron binding energy was kept finite. The present calculation is extended to finite coupling strengths. This introduces dispersion in the lattice deformation parameters, leads to lower ground-state energy and produces weakest renormalisation of the tunnelling matrix element.