Effective Hamiltonians to Describe Octahedral Tilt Instabilities in Halide Perovskites

Configurational cluster expansions, based on discrete occupation variables, have proven invaluable for constructing finite-temperature phase diagrams. Here, we develop a cluster expansion method to include continuous degrees of freedom. In this way we capture the effects of anharmonic interactions and high-temperature dynamic instabilities which are needed to describe structural phase transitions as a function of temperature. As a polynomial parameterization of the quantum mechanical zero Kelvin energy surface, the described effective Hamiltonians link \textit{ab initio }calculations to finite-temperature thermodynamics through Monte Carlo simulations. We present the methodology and apply it in a study of phase transitions in perovskite systems where symmetry breaking occurs through octahedral tilts.