Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

摘要: The self-consistent harmonic approximation is an effective theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved be efficient method study, from first-principles, properties solids. as a function average positions (centroids) can used study quantum or thermal lattice instability. In particular centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves ferroelectric instabilities. According Landau's theory, knowledge second derivative (i.e., curvature) respect high-symmetry configuration allows identification phase-transition instability modes. this work we derive exact analytic formula for generic configuration. expressed terms displacements forces form that evaluated by technique using importance sampling. Our approach particularly suitable applications based on first-principles density-functional-theory calculations, where atoms obtained negligible computational effort compared total determination. Finally, propose dynamical extension spectral phonons, probed inelastic scattering processes. We illustrate our numerical application toy model mimics transition rock-salt crystals SnTe GeTe.