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Strong repulsive interactions between electrons can lead to a Mottmetal-insulator transition. The Dynamical Mean-Field Theory (DMFT) explains thecritical end-point and hysteresis region with single-particle concepts such asthe spectral function and the quasiparticle weight. In this work, we reconsiderthe critical end point of the metal-insulator transition on the two-particlelevel. We show that the relevant eigenvalue and eigenvector of the non-localBethe-Salpeter kernel provide a unified picture of the hysteresis region and ofthe critical end point of the Mott transition. In particular, theysimultaneously explain the thermodynamics of the hysteresis region and theiterative stability of the DMFT equations. This analysis paves the way for adeeper understanding of phase transitions in correlated materials.

The Bethe-Salpeter equation at the critical end-point of the Mott transition