New Method Enhances Stability in Quantum Many-Body System Analysis

A new paper titled "Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems" has been published by authors Yuichi Motoyama, Hiroshi Shinaoka, Junya Otsuki, and Kazuyoshi Yoshimi. The paper addresses a significant challenge in the field of quantum many-body systems: the analytic continuation (AC) from imaginary-time Green's functions to spectral functions. This process is crucial for analyzing dynamical properties but is often unstable due to noise in the Green's function, particularly in multi-orbital systems where hybridization occurs between spin-orbitals.

The authors propose an advanced analytic continuation method that utilizes sparse modeling to mitigate the effects of noise and ensure the semi-positive definiteness of the spectral matrix. This is essential for satisfying causality in the analysis. The proposed method demonstrates enhanced stability and precision compared to conventional sparse modeling techniques, particularly when handling off-diagonal elements in Green's functions.

The findings of this research could have important implications for the numerical analysis of quantum systems, potentially leading to more reliable results in studies of strongly correlated electrons and other complex materials. The paper is available for reference on arXiv under the identifier arXiv:2409.01509.