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As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin’s G0W0 approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated."}],"publication":"Physical Review B","issue":"23","doi":"10.1103/PhysRevB.64.235106","article_number":"235106","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2022-11-11T06:54:19Z","article_type":"original","intvolume":"        64","year":"2001","title":"Diagrammatic self-energy approximations and the total particle number","publication_identifier":{"eissn":["1095-3795"],"issn":["0163-1829"]},"author":[{"id":"458","orcid":"0000-0002-4855-071X","first_name":"Arno","last_name":"Schindlmayr","full_name":"Schindlmayr, Arno"},{"full_name":"García-González, Pablo","first_name":"Pablo","last_name":"García-González"},{"full_name":"Godby, Rex William","first_name":"Rex William","last_name":"Godby"}],"oa":"1","external_id":{"arxiv":["cond-mat/0110435"],"isi":["000172867900050"]},"quality_controlled":"1","file_date_updated":"2020-08-30T16:15:45Z","isi":"1","citation":{"ieee":"A. Schindlmayr, P. García-González, and R. W. Godby, “Diagrammatic self-energy approximations and the total particle number,” <i>Physical Review B</i>, vol. 64, no. 23, Art. no. 235106, 2001, doi: <a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">10.1103/PhysRevB.64.235106</a>.","apa":"Schindlmayr, A., García-González, P., &#38; Godby, R. W. (2001). Diagrammatic self-energy approximations and the total particle number. <i>Physical Review B</i>, <i>64</i>(23), Article 235106. <a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">https://doi.org/10.1103/PhysRevB.64.235106</a>","chicago":"Schindlmayr, Arno, Pablo García-González, and Rex William Godby. “Diagrammatic Self-Energy Approximations and the Total Particle Number.” <i>Physical Review B</i> 64, no. 23 (2001). <a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">https://doi.org/10.1103/PhysRevB.64.235106</a>.","short":"A. Schindlmayr, P. García-González, R.W. Godby, Physical Review B 64 (2001).","mla":"Schindlmayr, Arno, et al. “Diagrammatic Self-Energy Approximations and the Total Particle Number.” <i>Physical Review B</i>, vol. 64, no. 23, 235106, American Physical Society, 2001, doi:<a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">10.1103/PhysRevB.64.235106</a>.","bibtex":"@article{Schindlmayr_García-González_Godby_2001, title={Diagrammatic self-energy approximations and the total particle number}, volume={64}, DOI={<a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">10.1103/PhysRevB.64.235106</a>}, number={23235106}, journal={Physical Review B}, publisher={American Physical Society}, author={Schindlmayr, Arno and García-González, Pablo and Godby, Rex William}, year={2001} }","ama":"Schindlmayr A, García-González P, Godby RW. Diagrammatic self-energy approximations and the total particle number. <i>Physical Review B</i>. 2001;64(23). doi:<a href=\"https://doi.org/10.1103/PhysRevB.64.235106\">10.1103/PhysRevB.64.235106</a>"},"user_id":"458","ddc":["530"],"volume":64,"_id":"18612","publisher":"American Physical Society","has_accepted_license":"1","status":"public"},{"type":"journal_article","file":[{"description":"© 2001 American Physical Society","date_created":"2020-08-28T21:37:22Z","creator":"schindlm","title":"Exchange-correlation kernels for excited states in solids","file_id":"18616","content_type":"application/pdf","relation":"main_file","date_updated":"2020-08-30T16:14:58Z","file_name":"PhysRevB.63.235106.pdf","file_size":257467,"access_level":"open_access"}],"date_created":"2020-08-28T21:35:45Z","abstract":[{"text":"The performance of several common approximations for the exchange-correlation kernel within time-dependent density-functional theory is tested for elementary excitations in the homogeneous electron gas. Although the adiabatic local-density approximation gives a reasonably good account of the plasmon dispersion, systematic errors are pointed out and traced to the neglect of the wave-vector dependence. Kernels optimized for atoms are found to perform poorly in extended systems due to an incorrect behavior in the long-wavelength limit, leading to quantitative deviations that significantly exceed the experimental error bars for the plasmon dispersion in the alkali metals.","lang":"eng"}],"extern":"1","issue":"23","publication":"Physical Review B","doi":"10.1103/PhysRevB.63.235106","article_number":"235106","language":[{"iso":"eng"}],"date_updated":"2022-11-11T06:55:14Z","publication_status":"published","intvolume":"        63","article_type":"original","title":"Exchange-correlation kernels for excited states in solids","year":"2001","author":[{"last_name":"Tatarczyk","first_name":"Krzysztof","full_name":"Tatarczyk, Krzysztof"},{"id":"458","first_name":"Arno","orcid":"0000-0002-4855-071X","last_name":"Schindlmayr","full_name":"Schindlmayr, Arno"},{"full_name":"Scheffler, Matthias","first_name":"Matthias","last_name":"Scheffler"}],"publication_identifier":{"issn":["0163-1829"],"eissn":["1095-3795"]},"oa":"1","external_id":{"arxiv":["cond-mat/0103357"],"isi":["000169459300035"]},"quality_controlled":"1","file_date_updated":"2020-08-30T16:14:58Z","citation":{"ieee":"K. Tatarczyk, A. Schindlmayr, and M. Scheffler, “Exchange-correlation kernels for excited states in solids,” <i>Physical Review B</i>, vol. 63, no. 23, Art. no. 235106, 2001, doi: <a href=\"https://doi.org/10.1103/PhysRevB.63.235106\">10.1103/PhysRevB.63.235106</a>.","apa":"Tatarczyk, K., Schindlmayr, A., &#38; Scheffler, M. (2001). 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Tatarczyk, A. Schindlmayr, M. Scheffler, Physical Review B 63 (2001).","ama":"Tatarczyk K, Schindlmayr A, Scheffler M. Exchange-correlation kernels for excited states in solids. <i>Physical Review B</i>. 2001;63(23). doi:<a href=\"https://doi.org/10.1103/PhysRevB.63.235106\">10.1103/PhysRevB.63.235106</a>"},"isi":"1","ddc":["530"],"user_id":"458","volume":63,"publisher":"American Physical Society","_id":"18615","has_accepted_license":"1","status":"public"},{"quality_controlled":"1","citation":{"apa":"Schindlmayr, A. (2001). Self-consistency and vertex corrections beyond the GW approximation. In S. G. Pandalai (Ed.), <i>Recent Research Developments in Physics</i> (Vol. 2, pp. 277–288). Transworld Research Network.","ieee":"A. Schindlmayr, “Self-consistency and vertex corrections beyond the GW approximation,” in <i>Recent Research Developments in Physics</i>, vol. 2, S. G. Pandalai, Ed. 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Beck}, author={Lloyd, Geoffrey}, editor={Fried, Johannes and Süßmann, Johannes, Süßmann, Johannes}, year={2001}, pages={96–115}, collection={Beck’sche Reihe} }","mla":"Lloyd, Geoffrey. “Wissenschaft und Gesellschaft in antiken Kulturen.” <i>Revolutionen des Wissens. Von der Steinzeit bis zur Moderne</i>, edited by Johannes Fried and Johannes Süßmann, translated by Johannes Süßmann, vol. 1450, C.H. Beck, 2001, pp. 96–115.","short":"G. Lloyd, in: J. Fried, J. Süßmann (Eds.), Revolutionen des Wissens. Von der Steinzeit bis zur Moderne, C.H. Beck, München, 2001, pp. 96–115.","chicago":"Lloyd, Geoffrey. “Wissenschaft und Gesellschaft in antiken Kulturen.” In <i>Revolutionen des Wissens. Von der Steinzeit bis zur Moderne</i>, edited by Johannes Fried and Johannes Süßmann, translated by Johannes Süßmann, 1450:96–115. Beck’sche Reihe. München: C.H. Beck, 2001.","apa":"Lloyd, G. (2001). Wissenschaft und Gesellschaft in antiken Kulturen. In J. Fried &#38; J. Süßmann (Eds.), &#38; J. 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