Correlation-driven phonon renormalisation and the equation of state of $\gamma$-cerium

Abstract

We investigate the thermodynamic properties of elemental cerium by assessing the crucial role of phonon free energy within the framework of dynamical mean-field theory (DMFT). While conventional density functional theory (DFT) often fails to capture the intricate energy landscape of $f$-electron materials, our approach integrates many-body electronic correlations with lattice dynamics to achieve a more rigorous description of the equation of state. We calculate the total energy as a function of the lattice constant at both the DFT and DFT+DMFT levels, subsequently incorporating the vibrational free energy derived from the phonon density of states. Our findings reveal that electronic renormalisation of the force constants significantly alters the phonon spectra, particularly in the strongly correlated $\gamma$-phase. By applying these phonon corrections to the energy profiles, we observe a substantial refinement in the predicted equilibrium volumes. Using principal-component-based machine learning, we interpolate phonon dispersions continuously from a finite set of first-principles calculations and compare them to experiment, finding significantly closer agreement compared to conventional DFT and DFT+U calculations that neglect dynamical many-body correlations. This study underlines the necessity of accounting for both electronic and vibrational entropy when evaluating the phase stability and structural transitions of lanthanide systems under varying pressures and temperatures.

12 pages, 6 figures

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