Prediction of First-Order Phase Transition with Electron−PhononInteraction

Phase transitions in solids occur due to the shifting balance between thebinding energies and entropic contributions of different crystal structures, even though theunderlying Hamiltonian remains the same. This work demonstrates that incorporatingelectron−phonon interactions in the Hamiltonian results in distinct free energies atdifferent temperatures, thus leading to a first-order phase transition. Contrary to priorinvestigations, taking into consideration the quantum mechanical kinetic energy operatorof the nucleus by employing Bogoliubov’s inequality yields a first-order phase transition.An equation is implicitly derived to determine the critical temperature of the first-order phase transition. Furthermore, an estimationis made to evaluate the latent heat and the resulting positional displacement of the nucleus. Comparing the present findings withprevious ones allows setting parameter boundaries for both first- and second-order phase transitions.