Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems

TL;DR

This paper introduces a robust analytic continuation method for multi-orbital quantum systems that employs sparse modeling and enforces semi-positive definiteness, improving stability and accuracy over traditional approaches.

Contribution

The paper presents a novel sparse modeling-based analytic continuation technique that explicitly imposes semi-positive definiteness for multi-orbital systems, addressing noise sensitivity and causality constraints.

Findings

Enhanced stability and precision compared to conventional methods

Effective handling of off-diagonal Green's functions

Improved robustness against noise in spectral reconstruction

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.