Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems
Year: 2024
Type: preprint
Abstract: Analytic continuation (AC) from imaginary-time Green's function to spectral function is essential in the numerical analysis of dynamical properties in quantum many-body systems. However, this process faces a fundamental challenge: it is an ill-posed problem, leading to unstable spectra against the noise in the Green's function. This instability is further complicated in multi-orbital systems with hybridization between spin-orbitals, where off-diagonal Green's functions yield a spectral matrix with off-diagonal elements, necessitating the matrix's semi-positive definiteness to satisfy the causality. We propose an advanced AC method using sparse modeling for multi-orbital systems, which reduces the effect of noise and ensures the matrix's semi-positive definiteness. We demonstrate the effectiveness of this approach by contrasting it with the conventional sparse modeling method, focusing on handling Green's functions with off-diagonal elements, thereby demonstrating our proposed method's enhanced stability and precision.
Source: arXiv (Cornell University)
Institutions: The University of Tokyo, Saitama University, Okayama University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Development of an analytic continuation method with guaranteed accuracy using information theory, G1538374105, Development of theories for strongly correlated materials design, Extension and demonstration of two-particle-level computational theory based on dimensionality reduction to nonlocal electron correlation effects, G4910293609, First-principles calculations of two-particle response realized by dimensionality reduction, G6430560525
OpenAlex ID: W4402954843