Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function

The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be constructed by decomposing its spectral representation. We investigate the performance of this so-called intermediate representation (IR) from several points of view. First, we develop an efficient algorithm for computing the IR basis functions of arbitrary high degree. Second, for two simple models, we study the number of coefficients required to represent the Green's function within a given tolerance. We show that the number of coefficients grows only as O(lnβ) for fermions and converges to a constant for bosons as temperature T=1/β decreases. Third, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions on the real-frequency axis have features whose width is scaled as O(T), which is consistent with the low-T properties of quasiparticles in a Fermi liquid state. On the other hand, the properties of the bosonic basis functions are consistent with those of spin/orbital susceptibilities at low T. These results demonstrate the potential wide applications of the IR to calculations of correlated systems.