Andrea Ferretti, Tommaso Chiarotti, Nicola Marzari
{"title":"利用过极总和表示法进行格林函数嵌入","authors":"Andrea Ferretti, Tommaso Chiarotti, Nicola Marzari","doi":"10.1103/physrevb.110.045149","DOIUrl":null,"url":null,"abstract":"In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. The latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mtext>Tr</mtext><mi>ω</mi></msub><mtext>ln</mtext><mrow><mo>{</mo><msubsup><mi>G</mi><mn>0</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mi>G</mi><mo>}</mo></mrow></mrow></math>, where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mtext>Tr</mtext><mi>ω</mi></msub></math> is the integration in frequency of the trace operator. Here, we show that using a sum-over-poles representation for the Green's functions and the algorithmic-inversion method one can obtain, in full generality, an explicit analytical expression for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mtext>Tr</mtext><mi>ω</mi></msub><mtext>ln</mtext><mrow><mo>{</mo><msubsup><mi>G</mi><mn>0</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mi>G</mi><mo>}</mo></mrow></mrow></math>. Further, this allows us (1) to recover an explicit expression for the random phase approximation correlation energy in the framework of the optimized effective potential and (2) to derive a variational expression for the Klein functional valid in the presence of an embedding bath.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Green's function embedding using sum-over-pole representations\",\"authors\":\"Andrea Ferretti, Tommaso Chiarotti, Nicola Marzari\",\"doi\":\"10.1103/physrevb.110.045149\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. The latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msub><mtext>Tr</mtext><mi>ω</mi></msub><mtext>ln</mtext><mrow><mo>{</mo><msubsup><mi>G</mi><mn>0</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mi>G</mi><mo>}</mo></mrow></mrow></math>, where <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mtext>Tr</mtext><mi>ω</mi></msub></math> is the integration in frequency of the trace operator. Here, we show that using a sum-over-poles representation for the Green's functions and the algorithmic-inversion method one can obtain, in full generality, an explicit analytical expression for <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msub><mtext>Tr</mtext><mi>ω</mi></msub><mtext>ln</mtext><mrow><mo>{</mo><msubsup><mi>G</mi><mn>0</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mi>G</mi><mo>}</mo></mrow></mrow></math>. Further, this allows us (1) to recover an explicit expression for the random phase approximation correlation energy in the framework of the optimized effective potential and (2) to derive a variational expression for the Klein functional valid in the presence of an embedding bath.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.045149\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.045149","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Green's function embedding using sum-over-pole representations
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. The latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form , where is the integration in frequency of the trace operator. Here, we show that using a sum-over-poles representation for the Green's functions and the algorithmic-inversion method one can obtain, in full generality, an explicit analytical expression for . Further, this allows us (1) to recover an explicit expression for the random phase approximation correlation energy in the framework of the optimized effective potential and (2) to derive a variational expression for the Klein functional valid in the presence of an embedding bath.
期刊介绍:
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