Algorithmic Matsubara integration for Hubbard-like models
Amir Taheridehkordi, Stephanie H. Curnoe, James P.F. LeBlanc · Physical review. B./Physical review. B · 2019
We present an algorithm to evaluate Matsubara sums for Feynman diagrams composed of bare Green's functions with single-band dispersions and local $U$ Hubbard interaction vertices. The algorithm provides an exact construction of the analytic result for the frequency integrals of a diagram that can then be evaluated for all parameters $U$, temperature $T$, chemical potential $\ensuremath{\mu}$, external frequencies, and internal/external momenta. This method allows for symbolic analytic continuation of results to the real frequency axis, avoiding any ill-posed numerical procedure. This method can also be used to simultaneously evaluate diagrams throughout the entire $T\text{\ensuremath{-}}U\text{\ensuremath{-}}\ensuremath{\mu}$ phase space of Hubbard-like models even in the $T=0$ limit at minimal computational expense.