Nonlinear feedback effects in coupled boson-fermion systems - art. no. 134505

We address ourselves to a class of systems composed of two coupled subsyste ms without any intrasubsystem interaction: itinerant fermions and localized bosons on a lattice. Switching on an interaction between the two subsystem s leads to feedback effects which result in a rich dynamical structure in b oth of them. Such feedback features are studied on the basis of the flow eq uation technique-an infinite series of infinitesimal unitary transformation s-which leads to a gradual elimination of the intersubsystem interaction. A s a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the intersub system interaction a charge exchange term, -the boson-fermion model-the ini tially localized bosons acquire itinerancy through their dependence on the renormalized fermion dispersion. This latter evolves from a free particle d ispersion into one showing a pseudogap structure near the chemical potentia l. Upon lowering the temperature both subsystems simultaneously enter a mac roscopic coherent quantum state. The bosons become superfluid, exhibiting a soundwavelike dispersion while the fermions develop a true gap in their di spersion. The essential physical features described by this technique are a lready contained in the renormalization of the kinetic terms in the respect ive Hamiltonians of the two subsystems. The extra interaction terms resulti ng in the process of iteration only strengthen this physics. We compare the results with previous calculations based on self-consistent perturbative a pproaches.