Periodized Thermal Greens Functions and Applications

Abstract: This work describes a new formalism for Fermionic thermal Greens functions that are discretized in imaginary time. The discretization makes the thermal Greens function periodic in imaginary (Matsubara) frequency space and requires a generalisation of the Dyson equation and Luttinger-Ward-Baym-Kadanoff functional. A Pade method is used to perform an analytic continuation of the periodized Matsubara Greens function to real frequencies which conserves the spectral weight and thus the discontinuity of the corresponding real time Greens function at t = 0. Due to the Matsubara Greens function periodicity, the discrete imaginary frequency space is relatively small which allows calculations at the extremely high precision which is necessary to perform a reliable Pade fit. We use the method to compute the single particle spectral function and energy loss function for doped bilayer graphene in the two-band limit, described by parabolic dispersion and Coulomb interaction. Calculations are performed in both the random phase approximation (RPA) and the fully self-consistent GW approximation. The formalism is also applied to dynamical mean field the- ory calculations using iterated perturbation theory (IPT) for the paramagnetic Hubbard model.