Theory of core-level photoemission and the x-ray edge singularity across the Mott transition

The zero-temperature core-level photoemission spectrum of a Hubbard system is studied across the metal to Mott insulator transition using dynamical mean-field theory and Wilson's numerical renormalization group [Rev. Mod. Phys. 47, 773 (1975)]. An asymmetric power-law divergence is obtained in the metallic phase with an exponent α(U,Q)-1, which depends on the strength of both the Hubbard interaction U and the core-hole potential Q. For QUc∕2, α decreases with increasing U and vanishes at the transition (U→Uc) leading to a symmetric peak in the insulating phase. For QUc∕2, α remains finite, close to the transition, but the integrated intensity of the power law vanishes and there is no associated peak in the insulator. The weight and position of the remaining peaks in the spectra can be understood within a molecular orbital approach.