Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
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DOI：
10.1103/physrevb.98.035104
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发表时间：
2018-03
影响因子：
3.7
通讯作者：
Naoya Chikano;J. Otsuki;H. Shinaoka
中科院分区：
文献类型：
--
作者：
Naoya Chikano;J. Otsuki;H. Shinaoka
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.
