Charge-density-wave-gap formation in the two-dimensional Holstein model at half-filling

Abstract

We use 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 two-dimensional Holstein model. From QMC data for the dressed unequal-time Green’s function G(τ,p) we calculate the real frequency spectral function A(ω,p) for different temperatures T, electron-phonon coupling constants g, phonon frequencies ${\mathrm{\omega }}_0$, and spatial lattice sizes N. We also compute the spectral functions by approximate diagrammatic methods and find these results to be in good qualitative agreement with the QMC results. We discuss attempts to get quantitative agreement for a range of T and ${\mathrm{\omega }}_0$ by using a single renormalized vertex g¯ in place of g, an approach that proved useful in previous studies of the Hubbard model. Finally, comparisons are made with previous estimates of the CDW transition temperature based on measurements of static correlation functions and susceptibilities.