Analytical continuation of matrix-valued functions: Carathéodory formalism

Fei, Jiani; Yeh, Chia-Nan; Zgid, Dominika; Gull, Emanuel

doi:10.1103/physrevb.104.165111

Analytical continuation of matrix-valued functions: Carathéodory formalism

Journal Article · Wed Oct 06 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.165111· OSTI ID:1979671

^[1]; Yeh, Chia-Nan ^[2]; Zgid, Dominika ^[2]; ^[2]

Univ. of Michigan, Ann Arbor, MI (United States); OSTI
Univ. of Michigan, Ann Arbor, MI (United States)

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

View Accepted Manuscript (DOE)

Research Organization:: Emory Univ., Atlanta, GA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019374

OSTI ID:: 1979671

Alternate ID(s):: OSTI ID: 1824703

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 16 Vol. 104; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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