Prediction of First-Order Phase Transition with Electron-Phonon Interaction

Phase transitions in solids occur due to the shifting balance between the binding energies and entropic contributions of different crystal structures, even though the underlying Hamiltonian remains the same. This work demonstrates that incorporating electron-phonon interactions in the Hamiltonian results in distinct free energies at different temperatures, thus leading to a first-order phase transition. Contrary to prior investigations, taking into consideration the quantum mechanical kinetic energy operator of 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 estimation is made to evaluate the latent heat and the resulting positional displacement of the nucleus. Comparing the present findings with previous ones allows setting parameter boundaries for both first- and second-order phase transitions.