We also used a combination of Quantum Monte Carlo (QMC) methods and analytic continuation techniques to study the formation of charge density wave (CDW) gaps at half-filling in the 2-dimensional Holstein model. >From QMC data for the dressed unequal time Green's function G(tau,p) we calculate the real frequency spectral function A(omega,p) for different temperatures T, electron-phonon coupling constants g, phonon frequencies omega0, and spatial lattice sizes N. We also computed the spectral functions by approximate diagrammatic methods and found these results to be in good qualitative aggreement with the QMC results. We discussed attempts to get quantitative agreement for a range of T, omega0 by using a single renormalized vertex gbar in place of g, an approach that proved useful in previous studies of the Hubbard model. Finally, comparisons were made with previous estimates of the CDW transition temperature based on measurements of static correlation functions and susceptibilities.
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