Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

Abstract

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameter within the dynamical mean-field theory (DMFT). At the Mott transition the symmetric Landau parameter diverges, while the anti-symmetric one remains finite. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid, expressing the static response of individual electronic states through the dynamic response and a remainder. In the charge sector the remainder vanishes at the Mott transition, the static charge response of the Hubbard bands is thus given by the dynamic response.