Theory of excitation spectra of electron-phonon coupled systems

We present recent advances in understanding of the ground and excited states of the electron-phonon coupled systems obtained by novel methods of Diagrammatic Monte Carlo and Stochastic Optimization, which enable the approximation-free calculation of Matsubara Green function in imaginary times and perform unbiased analytic continuation to real frequencies. We analyze Rashba-Pekar exciton-polaron as a classic example of a system with self-trapping crossover and demonstrate basic features of the phenomenon. Analysis of unconventional self-trapping cases, such as Jahn-Teller driven crossover in one-dimensional systems and magnon-assisted localization in cuprates, is presented. Results on the optical conductivity of the Frohlich polaron are also discussed.