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 Mont...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 theτdomain,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 theτdomain is advantageous for many reasons and opens up multiple avenues for future applications.展开更多
基金supported partially by the Center for Advanced Systems Understanding(CASUS),which is financed by Germany’s Federal Ministry of Education and Research(BMBF),and by the state government of Saxony from the State budget approved by the Saxon State Parliament.This work has received funding from the European Research Council(ERC)under the European Union’s Horizon 2022 research and innovation program(Grant No.101076233,“PREXTREME”)The PIMC calculations were carried out at the Norddeutscher Verbund für Hoch-und Höchstleistungsrechnen(HLRN)under Grant No.shp00026,and on a Bull Cluster at the Center for Information Services and High Performance Computing(ZIH)at Technische Universität Dresden.
文摘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 theτdomain,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 theτdomain is advantageous for many reasons and opens up multiple avenues for future applications.
