Simulating the anharmonic phonon spectrum in critical systems: self-consistent phonons and temperature-dependent effective potential methods

TL;DR

This paper compares and improves methods for simulating anharmonic phonon spectra near critical points in materials, highlighting their limitations and proposing a new implementation for better accuracy in dynamical properties.

Contribution

It establishes guidelines for the accuracy of SCHA, SCP, and TDEP methods near critical points and introduces a corrected TDEP implementation for dynamical spectra.

Findings

Benchmarking against exact and real materials shows method limitations.

New TDEP implementation restores correct perturbative limits.

Guidelines for method accuracy on thermodynamic and dynamical properties.

Abstract

Understanding and simulating the thermodynamic and dynamical properties of materials affected by strong ionic anharmonicity is a central challenge in material science. Much interest is in material displaying critical displacive behaviour, such as near a ferroelectric transition, charge-density waves, or in general displacive second-order transitions. In these cases, molecular dynamics suffer from a critical slowdown and emergent long-range fluctuations of the order parameter. Two prominent methods have emerged to solve this issue: Self-consistent renormalization of the phonons like the Self-Consistent Harmonic Approximation (SCHA) and Self-Consistent Phonons (SCP), and methods that fit the potential energy landscape from short molecular dynamics trajectories, like the Temperature-Dependent Effective Potential (TDEP). Despite their widespread use, the limitations of these methods are often overlooked in the proximity of critical points. Here, we establish a guiding rule set for the accuracy of each method on critical quantities: free energy for computing the phase diagrams, static correlation functions for inferring phase stability and critical behaviours, and dynamic correlation functions for vibrational spectra and thermal transport. Also, a new TDEP implementation is introduced to fix the calculation of dynamical spectra, restoring the correct perturbative limit violated by the standard TDEP approach. Results are benchmarked both against an exact one-dimensional anharmonic potential and two prototypical anharmonic crystals: the ferroelectric PbTe and the metal-halide perovskite CsSnI3.