  The occurrence of thermal transport phenomena is widespread, exerting a
pivotal influence on the functionality of diverse electronic and
thermo-electric energy-conversion devices. The traditional first-principles
theory governing the thermal and thermodynamic characteristics of insulators
relies on the perturbative treatment of interatomic potential and ad-hoc
displacement of atoms within supercells. However, the limitations of these
approaches for highly anharmonic and weakly bonded materials, along with
discrepancies arising from not considering explicit finite temperature effects,
highlight the necessity for a well-defined quasiparticle approach to the
lattice vibrations. To address these limitations, we present a comprehensive
numerical framework in this study, designed to compute the thermal and
thermodynamic characteristics of crystalline semiconductors and insulators. The
self-consistent phonon renormalization method we have devised reveals phonons
as quasiparticles, diverging from their conventional characterization as bare
normal modes of lattice vibration. The extension of the renormalization impact
to interatomic force constants (IFCs) of third and fourth orders is also
integrated and demonstrated. For the comprehensive physical insights, we
employed an iterative solution of the Peierls-Boltzmann transport equation
(PBTE) to determine thermal conductivity and carry out Helmholtz free energy
calculations, encompassing anharmonicity effects up to the fourth order. In
this study, we utilize our numerical framework to showcase its applicability
through an examination of phonon dispersion, phonon linewidth, anharmonic
phonon scattering, and temperature-dependent lattice thermal conductivity in
both highly anharmonic materials (NaCl and AgI) and weakly anharmonic materials
(cBN and 3C-SiC).
