Revisit Many-body Interaction Heat Current and Thermal Conductivity Calculation in Moment Tensor Potential/LAMMPS Interface

TL;DR

This study investigates the impact of many-body interactions on heat current calculations and thermal conductivity in molecular dynamics simulations using Moment Tensor Potentials, revealing significant discrepancies and the need for revised models.

Contribution

It identifies the lack of a generalized many-body heat current description in MLPs and proposes revisions that significantly affect thermal conductivity results.

Findings

Inconsistencies found between thermostat and heat current operator violating energy conservation.

Revising the heat current formula alters thermal conductivity by 29-64%.

Highlights the importance of many-body effects in thermal analysis with MLPs.

Abstract

The definition of heat current operator for systems for non-pairwise additive interactions and its impact on related lattice thermal conductivity ($\kappa_{L}$) via molecular dynamics simulation (MD) are ambiguous and controversial when migrating from conventional empirical potential models to machine learning potential (MLP) models. Empirical model descriptions are often limited to three- to four-body interaction while a sophisticated representation of the many-body physics could be resembled in MLPs. Herein, we study and compare the significance of many-body interaction to the heat current computation in one of the most popular MLP models, the Moment Tensor Potential (MTP). Non-equilibrium MD simulations and equilibrium MD simulations among four different materials, $PbTe$, amorphous $Sc_{0.2}Sb_{2}Te_{3}$, graphene, and $BAs$, were performed. We found inconsistency between the simulation thermostat and its implemented heat current operator in our non-equilibrium MD results which violate law of energy conservation and suggest a need for revision. We revisit the virial stress tensor expression within the calculator and identified the lack of a generalised many-body heat current description in it. We uncover the influence of the modified heat current formula that could alter the $\kappa_{L}$ results 29% to 64% using the equilibrium MD computational approach. Our work demonstrates the importance of a many-body description during thermal analysis in MD simulations when MLPs are in concern. This work sheds light on a better understanding of the relationship between interatomic interaction and its heat transport mechanism.