Abstract Ostlund et al

S. Ostlund et al.

Discretized thermal Green's functions

We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time $\tau$ and thus periodic in imaginary (``Matsubara'') frequency $i\omega_n$.  The formalism requires a generalization of the Dyson equation $G(G_0,\Sigma)$ and the Baym-Kadanoff-Luttinger-Ward functional for the free energy $\beta\Omega=\Gamma(G)$.  A conformal transformation is used to analytically continue the periodized Matsubara Green's function to real frequencies in a way that conserves the discontinuity at $t=0$ of the corresponding real-time Green's function. This allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation in the $\tau$ discretization. The formalism is tested on dynamical mean field theory calculations of the paramagnetic Hubbard model.