Green’s-function self-energies in the two-dimensional Holstein model

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Abstract
We examine the behavior of the electron and phonon self-energies obtained from quantum Monte Carlo simulations of the two-dimensional Holstein model as a function of Matsubara frequency and momentum. For the half-filled system, there is a finite-temperature phase transition to an insulating charge-density-wave state, and the electron self-energy develops a distinctive divergence. The renormalized phonon frequency softens strongly with temperature at the commensurate wave vector. Away from half-filling, the electron self-energy behaves in a manner consistent with that of a Fermi liquid.