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

TL;DR

This paper evaluates the intermediate orthogonal representation of imaginary-time Green's functions, showing its efficiency and physical relevance for modeling correlated electron systems at various temperatures.

Contribution

It provides a detailed performance analysis of the physically constructed intermediate representation, highlighting its temperature-dependent coefficient growth and physical basis properties.

Findings

Number of coefficients grows as O(log β) for fermions

Coefficients converge to a constant for bosons at low T

Basis functions reflect physical properties of quasiparticles and susceptibilities

Abstract

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 \textit{intermedaite representation} (IR) from several points of view. First, for two simple models, we study the number of coefficients necessary to achieve a given tolerance in expanding the Green's function. We show that the number of coefficients grows only as $O(\log \beta)$ for fermions, and converges to a constant for bosons as temperature $T=1/\beta$ decreases. Second, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions have features in the spectrum whose width is scaled as $O(T)$, which are 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 application of the IR to calculations of correlated systems.