Physical insights from imaginary-time density–density correlation functions

Dornheim Tobias; Moldabekov Zhandos A.; Tolias Panagiotis; Böhme Maximilian; Vorberger Jan

doi:10.1063/5.0149638

Volume 8 Issue 5

Sep. 2023

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Dornheim Tobias, Moldabekov Zhandos A., Tolias Panagiotis, Böhme Maximilian, Vorberger Jan. Physical insights from imaginary-time density–density correlation functions[J]. Matter and Radiation at Extremes, 2023, 8(5): 056601. doi: 10.1063/5.0149638

Citation:

Dornheim Tobias, Moldabekov Zhandos A., Tolias Panagiotis, Böhme Maximilian, Vorberger Jan. Physical insights from imaginary-time density–density correlation functions[J]. Matter and Radiation at Extremes, 2023, 8(5): 056601. doi: 10.1063/5.0149638

Citation:

Dornheim Tobias, Moldabekov Zhandos A., Tolias Panagiotis, Böhme Maximilian, Vorberger Jan. Physical insights from imaginary-time density–density correlation functions[J]. Matter and Radiation at Extremes, 2023, 8(5): 056601. doi: 10.1063/5.0149638

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Physical insights from imaginary-time density–density correlation functions

doi: 10.1063/5.0149638

1.
Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
2.
Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
3.
Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
4.
Technische Universität Dresden, D-01062 Dresden, Germany

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Corresponding author: a)Author to whom correspondence should be addressed: t.dornheim@hzdr.de
Received Date: 2023-03-07
Accepted Date: 2023-07-11

Available Online: 2023-09-01

Publish Date: 2023-09-01

Abstract

Abstract

An accurate theoretical description of the dynamic properties of correlated quantum many-body systems, such as the dynamic structure factor S( q , ω), is important in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary-time density–density correlation function F( q , τ) to real frequencies is a notoriously hard problem. Here, it is argued that often no such analytic continuation is required because by definition, F( q , τ) contains the same physical information as does S( q , ω), only represented unfamiliarly. Specifically, it is shown how one can directly extract key information such as the temperature or quasi-particle excitation energies from the τ domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions [T. Dornheim et al., Nat. Commun. 13 , 7911 (2022)]. As a practical example, ab initio path-integral Monte Carlo results for the uniform electron gas (UEG) are considered, and it is shown that even nontrivial processes such as the roton feature of the UEG at low density [T. Dornheim et al., Commun. Phys. 5 , 304 (2022)] are manifested straightforwardly in F( q , τ). A comprehensive overview is given of various useful properties of F( q , τ) and how it relates to the usual dynamic structure factor. In fact, working directly in the τ domain is advantageous for many reasons and opens up multiple avenues for future applications.

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