Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Huang, Zhen; Gull, Emanuel; Lin, Lin

doi:10.1103/physrevb.107.075151

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Journal Article · Thu Feb 23 00:00:00 EST 2023 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.107.075151· OSTI ID:2234182

Huang, Zhen ^[1]; ^[2]; Lin, Lin ^[3]

University of California, Berkeley, CA (United States)
University of Michigan, Ann Arbor, MI (United States)
University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: US Air Force Office of Scientific Research (AFOSR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231; SC0022088; SC0022198

OSTI ID:: 2234182

Alternate ID(s):: OSTI ID: 1958321

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 7 Vol. 107; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

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