Guaranteed Accuracy Formalism for Imaginary Time Calculations*

Finite-temperature Green's function calculations of quantum systems are frequently performed in the Matsubara formalism, with calculation steps alternating between imaginary time steps (e.g. solution of a lattice model) and Matsubara frequencies (e.g. solution of a Dyson equation). In large systems, these transforms and the ill-conditioned nature of the Matsubara equations often lead to the amplification of small roundoff and cutoff errors.
In this talk I will show how calculations can be performed in imaginary time only. Error accumulation from Fourier transforms can thereby be avoided, and accuracy guarantees can be given for all calculation steps.