# CMT seminar: Collective excitations of strongly correlated electrons, vertex corrections and gauge invariance

Thursday, March 13, 2014 – 1:30pm – 3:00pm

Regents 351

Hartmut Hafermann

Center of theoretical physics, Ecole Polytechnic, Paris

In this talk, I consider the collective, long-wavelength charge excitations in correlated media in presence of short- and long-range forces.

The two-dimensional Hubbard model is examined exemplary for the case of a short-range interaction. While the random phase approximation yields a zero sound mode expected for short-range forces, it does not capture the Mott physics. The latter can be described within dynamical mean-field theory (DMFT). I will show that non-local vertex corrections included in the DMFT susceptibility are essential in order to fulfill the Ward identity and to yield a manifestly gauge invariant response in finite dimensions. The relation between the vertex corrections, gauge invariance and the appearance of the collective modes is discussed.

Models with long-range interaction can be treated within extended dynamical mean-field theory (EDMFT). The EDMFT susceptibility, however, does not respect the Ward identity and hence does not provide a valid description of plasmons. The recently proposed dual boson approach, which may be viewed as a diagrammatic extension of EDMFT, allows one to systematically include non-local vertex corrections beyond EDMFT. I will show that these corrections act to restore the gauge invariance of the theory and resolve an inconsistency in the calculation of susceptibilities within EDMFT. By comparing the energy of the collective modes with the plasma frequency, which is determined from single-particle properties as a consequence of gauge invariance, the collective excitations are identified as plasmons.

Host: Jim Freericks