Breakdown of Fermi Liquid Theory in Doped Mott Insulators by Dynamical Spectral Weight Transfer

We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge $2e$ boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge $2e$ boson binds to a hole, thereby mediating new charge $e$ states at low energy. It is the presence of such charge $e$ states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge $2e$ boson formulation and the standard perturbative treatment is explained.