Additional material#
References#
Lewin Boehnke, Hartmut Hafermann, Michel Ferrero, Frank Lechermann, and Olivier Parcollet. Orthogonal polynomial representation of imaginary-time Green’s functions. Physical Review B, 84(7):075145, 2011-08. doi:10.1103/physrevb.84.075145.
Mattia Bruno, Leonardo Giusti, and Matteo Saccardi. Spectral densities from Euclidean lattice correlators via the Mellin transform. Phys. Rev. D, 111:094515, 2025. doi:10.1103/PhysRevD.111.094515.
Naoya Chikano, Junya Otsuki, and Hiroshi Shinaoka. Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function. Physical Review B, 98(3):035104, 07 2018. doi:10.1103/physrevb.98.035104.
Naoya Chikano, Kazuyoshi Yoshimi, Junya Otsuki, and Hiroshi Shinaoka. irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function. Computer Physics Communications, 240:181–188, 2019. URL: https://www.sciencedirect.com/science/article/pii/S001046551930058X?via\%3Dihub, arXiv:1807.05237, doi:10.1016/j.cpc.2019.02.006.
Selina Dirnböck, Seung-Sup B. Lee, Fabian B. Kugler, Sebastian Huber, Jan von Delft, Karsten Held, and Markus Wallerberger. Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions. Phys. Rev. Research, 6:043228, 2024. doi:10.1103/PhysRevResearch.6.043228.
Shoji Hashimoto. Smeared spectral functions from lattice QCD: opportunities and challenges. 2026. arXiv:2609.02239, doi:10.48550/arXiv.2609.02239.
Merzuk Kaltak and Georg Kresse. Minimax isometry method: A compressive sensing approach for Matsubara summation in many-body perturbation theory. Physical Review B, 101(20):205145, 2020. arXiv:1909.01740, doi:10.1103/physrevb.101.205145.
Jason Kaye, Kun Chen, and Olivier Parcollet. Discrete lehmann representation of imaginary time green's functions. Phys. Rev. B, 105:235115, Jun 2022. URL: https://link.aps.org/doi/10.1103/PhysRevB.105.235115, doi:10.1103/PhysRevB.105.235115.
Jason Kaye, Kun Chen, and Hugo U. R. Strand. Libdlr: efficient imaginary time calculations using the discrete lehmann representation. Comput. Phys. Commun., 280:108458, 2022. doi:10.1016/j.cpc.2022.108458.
Dominik Kiese, Hugo U. R. Strand, Kun Chen, Nils Wentzell, Olivier Parcollet, and Jason Kaye. Discrete Lehmann representation of three-point functions. Phys. Rev. B, 111:035135, 2025. doi:10.1103/PhysRevB.111.035135.
Jia Li, Markus Wallerberger, Naoya Chikano, Chia-Nan Yeh, Emanuel Gull, and Hiroshi Shinaoka. Sparse sampling approach to efficient ab initio calculations at finite temperature. Physical Review B, 101(3):035144, 01 2020. doi:10.1103/physrevb.101.035144.
Takahiro Misawa. Analytic origin of Green-function compression in the intermediate representation. 2026. arXiv:2605.24814, doi:10.48550/arXiv.2605.24814.
Hitoshi Mori, Takuya Nomoto, Ryotaro Arita, and Elena R. Margine. Efficient anisotropic migdal-eliashberg calculations with an intermediate representation basis and wannier interpolation. Phys. Rev. B, 110:064505, Aug 2024. URL: https://link.aps.org/doi/10.1103/PhysRevB.110.064505, doi:10.1103/PhysRevB.110.064505.
Masayuki Ohzeki. Analytical singular-value structure of analytic-continuation kernels from Slepian information theory. 2026. arXiv:2605.26586, doi:10.48550/arXiv.2605.26586.
Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, and Kazuyoshi Yoshimi. Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data. Physical Review E, 95(6):061302(R), 06 2017. URL: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.95.061302, doi:10.1103/physreve.95.061302.
Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, and Kazuyoshi Yoshimi. Sparse Modeling in Quantum Many-Body Problems. Journal of the Physical Society of Japan, 89(1):012001, 01 2020. doi:10.7566/jpsj.89.012001.
Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, and Kazuyoshi Yoshimi. Efficient ab initio many-body calculations based on sparse modeling of matsubara green's function. 2021. URL: https://arxiv.org/abs/2106.12685, doi:10.48550/ARXIV.2106.12685.
Hiroshi Shinaoka, Dominique Geffroy, Markus Wallerberger, Junya Otsuki, Kazuyoshi Yoshimi, Emanuel Gull, and Jan Kuneš. Sparse sampling and tensor network representation of two-particle Green's functions. SciPost Physics, 8(1):012 – 23, 2020. URL: https://scipost.org/SciPostPhys.8.1.012/pdf, doi:10.21468/scipostphys.8.1.012.
Hiroshi Shinaoka and Yuki Nagai. Sparse modeling of large-scale quantum impurity models with low symmetries. Physical Review B, 103(4):045120, 2021. doi:10.1103/physrevb.103.045120.
Hiroshi Shinaoka, Junya Otsuki, Kristjan Haule, Markus Wallerberger, Emanuel Gull, Kazuyoshi Yoshimi, and Masayuki Ohzeki. Overcomplete compact representation of two-particle Green's functions. Physical Review B, 97(20):205111, 05 2018. URL: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.97.205111, doi:10.1103/physrevb.97.205111.
Hiroshi Shinaoka, Junya Otsuki, Masayuki Ohzeki, and Kazuyoshi Yoshimi. Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains. Physical Review B, 96(3):035147 – 8, 07 2017. URL: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.96.035147, doi:10.1103/physrevb.96.035147.
Hiroshi Shinaoka, Markus Wallerberger, Yuta Murakami, Kosuke Nogaki, Rihito Sakurai, Philipp Werner, and Anna Kauch. Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains. Phys. Rev. X, 13:021015, 2023. doi:10.1103/PhysRevX.13.021015.
Ryutaro Tsuji and Shoji Hashimoto. Spectral reconstruction from Euclidean lattice correlators through singular value decomposition. 2026. arXiv:2605.15674, doi:10.48550/arXiv.2605.15674.
Markus Wallerberger, Samuel Badr, Shintaro Hoshino, Fumiya Kakizawa, Takashi Koretsune, Yuki Nagai, Kosuke Nogaki, Takuya Nomoto, Hitoshi Mori, Junya Otsuki, Soshun Ozaki, Rihito Sakurai, Constanze Vogel, Niklas Witt, Kazuyoshi Yoshimi, and Hiroshi Shinaoka. sparse-ir: optimal compression and sparse sampling of many-body propagators. SoftwareX, 21:101266, 2023. doi:10.1016/j.softx.2022.101266.
Markus Wallerberger, Hiroshi Shinaoka, and Anna Kauch. Solving the Bethe-Salpeter equation with exponential convergence. Phys. Rev. Research, 3:033168, 2021. doi:10.1103/PhysRevResearch.3.033168.
Lei Zhang, André Erpenbeck, Yang Yu, and Emanuel Gull. Minimal pole representation for spectral functions. J. Chem. Phys., 162:214111, 2025. doi:10.1063/5.0273763.
Lei Zhang and Emanuel Gull. Minimal pole representation and controlled analytic continuation of matsubara response functions. Phys. Rev. B, 110:035154, 2024. doi:10.1103/PhysRevB.110.035154.
Lei Zhang, Yang Yu, and Emanuel Gull. Minimal pole representation and analytic continuation of matrix-valued correlation functions. Phys. Rev. B, 110:235131, 2024. doi:10.1103/PhysRevB.110.235131.