Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916379647541248 |
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| author | Motoyama, Yuichi Shinaoka, Hiroshi Otsuki, Junya Yoshimi, Kazuyoshi |
| author_facet | Motoyama, Yuichi Shinaoka, Hiroshi Otsuki, Junya Yoshimi, Kazuyoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems Motoyama, Yuichi Shinaoka, Hiroshi Otsuki, Junya Yoshimi, Kazuyoshi Strongly Correlated Electrons Statistical Mechanics Computational Physics 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. |
| title | Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems |
| topic | Strongly Correlated Electrons Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2409.01509 |