We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi-liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely, and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.
|Journal||Physical Review B|
|Publication status||Published - 2022 Dec 15|
Bibliographical noteFunding Information:
This work was supported by NRF of Korea (Grants No. 2020R1A2C3013673 and No. 2017R1A5A1014862) and the KISTI supercomputing center (Project No. KSC-2021-CRE-0384).
© 2022 American Physical Society.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics