Phase transition in a system with a strong electron–phonon interaction

We have studied the bound state of a conduction electron and the optical vibrations in an ionic crystal. Using a variational method we have obtained analytic expressions for the ground state energy and for the effective mass for the case of an arbitrarily large electron–phonon coupling constant α. We have shown that in the range of values 6.6 < α <9.7 there is a rearrangement of the ground state. For 6.6 > α the ground state is delocalized. For 6.6<α <9.7 the localized and delocalized states coexist, but the delocalized state lies at lower energy. For α > 9.7 the localized state lies lower. We briefly discuss the possibility for experimental observation of transitions between the free and self-localized states.

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