Isostructural α − γ phase transition in cerium from the perspective of metageneralized gradient approximations

Metageneralized gradient approximations (meta-GGAs) on the third rung of the functional hierarchy are gaining increasing relevance for electronic structures. Meta-GGAs are constructed from numerous ingredients including the orbital kinetic energy density that make them more flexible than generalized gradient approximations (GGAs) including the heavily used Perdew-Burke-Ernzerhof GGA (PBE-GGA). Still, most meta-GGAs cope with the expected limitations of a semilocal density functional when band gaps or localization of electrons are needed. On the other hand, meta-GGAs are explicit functionals of the orbitals. This feature resembles hybrid density functionals with exact exchange. Efforts in recent years demonstrate that some meta-GGAs can rise beyond the accuracy of semilocal approximations when band gaps are computed. Cerium is an ideal test bed to challenge some recent meta-GGAs. Cerium shows an isostructural $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$ phase transition with delocalized and localized $f$ electrons in each phase, respectively. The correlation of $f$ electron systems is hardly captured by semilocal approximations, but the recent Lebeda-Aschebrock-K\"ummel (LAK) meta-GGA with ultranonlocality steps out of the framework of conventional semilocal density functionals and delivers spectacular accuracy for the phase transition of cerium. LAK and further meta-GGAs inspired by the success of LAK can open a forefront of meta-GGAs for quantum materials with localized electrons.