Dynamical properties of SSH and breathing type Hamiltonians

Using a QMC method based on exact phonon integration in Fourier space and on loop updates in particle space, we study fermionic systems coupled to dynamical phonons in one dimension. Within this method it is possible to investigate Su-Schrieffer-Heeger (SSH) as well as Holstein type models, with momentum dependent couplings (e.g. breathing phonons) and arbitrary phonon dispersions. We access the dynamical properties of the systems via momentum dependent phonon spectral functions and electron Greens functions. In case of the standard Holstein model, we present precise data for the phonon spectral function in both the metallic Luttinger liquid and the insulating charge density wave phase, for a wide range of phonon frequencies.