Efficient Legendre representation of many-particle Green's functions

Even though a way of obtaining frequency and wave-vector-dependent lattice susceptibilities within the dynamical mean-field theory (DMFT) is known for some years, only very few calculations were actually performed. A reason therefore is the numerically expensive handling of the two-particle Green's function with respect to three slowly decaying frequency variables. Within quantum Monte-Carlo (QMC) methods, the latter fact renders the accumulation lengthy and leads to numerical instabilities in the further use of the obtained many-particle objects. We propose tailored representation of the one- and two-particle Green's function for an accurate QMC accumulation within the class of continuous-time impurity solvers for the DMFT approximation, based on the expansion of fermionic degrees of freedom in Legendre polynomials. This leads to a substantial increase in performance, allowing for the efficient calculation of spin and charge susceptibilities for canonical models as well as realistic materials over wide ranges of temperature, doping and interaction strength.