Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 92, Issue 7, 2015, Pages

  Ljungberg, M P ^a,b   Koval, P ^b   Ferrari, F ^b,c   Foerster, D ^d   Sanchez Portal D ^b,e  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b DONOSTIA INTERNATIONAL PHYSICS CENTER DIPC   (Spain)

^c UNIVERSITY OF MILANO BICOCCA   (Italy)

^d UMR 5798   (France)

^e CENTRO MIXTO CSIC UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84940063382     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.92.075422     Document Type: Article

References (78)

1. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.52.997
2. M. E. Casida, A. Ipatov, and F. Cordova, Time-Dependent Density Functional Theory (Springer, Heidelberg, 2006).
3. L. Hedin, Phys. Rev. 139, A796 (1965). PHRVAO 0031-899X 10.1103/PhysRev.139.A796
4. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.601
5. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Boston, 1971).
6. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963).
7. W. Hanke and L. J. Sham, Phys. Rev. B 21, 4656 (1980). PRBMDO 0163-1829 10.1103/PhysRevB.21.4656
8. F. Bechstedt, K. Tenelsen, B. Adolph, and R. Del Sole, Phys. Rev. Lett. 78, 1528 (1997). PRLTAO 0031-9007 10.1103/PhysRevLett.78.1528
9. X. Blase and C. Attaccalite, Appl. Phys. Lett. 99, 171909 (2011). APPLAB 0003-6951 10.1063/1.3655352
10. S. Albrecht, G. Onida, and L. Reining, Phys. Rev. B 55, 10278 (1997). PRBMDO 0163-1829 10.1103/PhysRevB.55.10278
11. P. Noziéres, Theory of Interacting Fermi Systems (Benjamin, New York, 1964).
12. L. J. Sham and T. M. Rice, Phys. Rev. 144, 708 (1966). PHRVAO 0031-899X 10.1103/PhysRev.144.708
13. E. L. Shirley and S. G. Louie, Phys. Rev. Lett. 71, 133 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.133
14. G. Onida, L. Reining, R. W. Godby, R. Del Sole, and W. Andreoni, Phys. Rev. Lett. 75, 818 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.75.818
15. L. X. Benedict, E. L. Shirley, and R. B. Bohn, Phys. Rev. Lett. 80, 4514 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.4514
16. L. X. Benedict, A. Puzder, A. J. Williamson, J. C. Grossman, G. Galli, J. E. Klepeis, J.-Y. Raty, and O. Pankratov, Phys. Rev. B 68, 085310 (2003). PRBMDO 0163-1829 10.1103/PhysRevB.68.085310
17. M. Palummo, O. Pulci, R. D. Sole, A. Marini, P. Hahn, W. G. Schmidt, and F. Bechstedt, J. Phys.: Condens. Matter 16, S4313 (2004). JCOMEL 0953-8984 10.1088/0953-8984/16/39/006
18. J. M. Garcia-Lastra, J. D. Bass, and K. S. Thygesen, J. Chem. Phys. 135, 121101 (2011). JCPSA6 0021-9606 10.1063/1.3645544
19. D. Rocca, D. Lu, and G. Galli, J. Chem. Phys. 133, 164109 (2010). JCPSA6 0021-9606 10.1063/1.3494540
20. M. Grüning, A. Marini, and X. Gonze, Comput. Mater. Sci. 50, 2148 (2011). CMMSEM 0927-0256 10.1016/j.commatsci.2011.02.021
21. L. E. Ramos, J. Paier, G. Kresse, and F. Bechstedt, Phys. Rev. B 78, 195423 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.195423
22. M. Gatti and F. Sottile, Phys. Rev. B 88, 155113 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.155113
23. L. X. Benedict and E. L. Shirley, Phys. Rev. B 59, 5441 (1999). PRBMDO 0163-1829 10.1103/PhysRevB.59.5441
24. A. Sitt, L. Kronik, S. Ismail-Beigi, and J. R. Chelikowsky, Phys. Rev. A 76, 054501 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.76.054501
25. M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 80, 3320 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.3320
26. M. E. Casida, J. Chem. Phys. 122, 054111 (2005). JCPSA6 0021-9606 10.1063/1.1836757
27. B. Baumeier, D. Andrienko, and M. Rohlfing, J. Chem. Theory Comput. 8, 2790 (2012). 1549-9618 10.1021/ct300311x
28. F. Bruneval and M. A. L. Marques, J. Chem. Theory Comput. 9, 324 (2013). 1549-9618 10.1021/ct300835h
29. P. Boulanger, D. Jacquemin, I. Duchemin, and X. Blase, J Chem Theory Comput. 10, 1212 (2014). 1549-9618 10.1021/ct401101u
30. C. Ambrosch-Draxl, K. Hummer, S. Sagmeister, and P. Puschnig, Chem. Phys. 325, 3 (2006), Electronic Processes in Organic Solids. CMPHC2 0301-0104 10.1016/j.chemphys.2005.11.038
31. J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, edited by Z. Bai (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000).
32. M. Valiev, E. Bylaska, N. Govind, K. Kowalski, T. Straatsma, H. V. Dam, D. Wang, J. Nieplocha, E. Apra, T. Windus, and W. de Jong, Comput. Phys. Commun. 181, 1477 (2010). CPHCBZ 0010-4655 10.1016/j.cpc.2010.04.018
33. Y. Saad, Iterative Methods for Sparse Linear Systems (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003).
34. P. Koval, D. Foerster, and O. Coulaud, J. Chem. Theory Comput. 6, 2654 (2010). 1549-9618 10.1021/ct100280x
35. R. Haydock, V. Heine, and M. J. Kelly, J. Phys. C: Solid State Phys. 5, 2845 (1972). JPSOAW 0022-3719 10.1088/0022-3719/5/20/004
36. D. Rocca, R. Gebauer, Y. Saad, and S. Baroni, J. Chem. Phys. 128, 154105 (2008). JCPSA6 0021-9606 10.1063/1.2899649
37. W. G. Schmidt, S. Glutsch, P. H. Hahn, and F. Bechstedt, Phys. Rev. B 67, 085307 (2003). PRBMDO 0163-1829 10.1103/PhysRevB.67.085307
38. C. Attaccalite, M. Grüning, and A. Marini, Phys. Rev. B 84, 245110 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.245110
39. L. X. Benedict (private communication).
40. C. Ochsenfeld, J. Kussmann, and D. S. Lambrecht, in Linear-Scaling Methods in Quantum Chemistry, Reviews in Computational Chemistry (Wiley, New York, 2007), pp. 1-82.
41. D. Neuhauser, E. Rabani, and R. Baer, J. Phys. Chem. Lett. 4, 1172 (2013). 1948-7185 10.1021/jz3021606
42. D. Neuhauser, Y. Gao, C. Arntsen, C. Karshenas, E. Rabani, and R. Baer, Phys. Rev. Lett. 113, 076402 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.076402
43. E. Rabani, R. Baer, and D. Neuhauser, Phys. Rev. B 91, 235302 (2015). PRBMDO 0163-1829 10.1103/PhysRevB.91.235302
44. J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón, and D. Sánchez-Portal, J. Phys.: Condens. Matter 14, 2745 (2002). JCOMEL 0953-8984 10.1088/0953-8984/14/11/302
45. D. Foerster, P. Koval, and D. Sánchez-Portal, J. Chem. Phys. 135, 074105 (2011). JCPSA6 0021-9606 10.1063/1.3624731
46. P. Koval, D. Foerster, and D. Sánchez-Portal, Phys. Rev. B 89, 155417 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.155417
47. D. Foerster, J. Chem. Phys. 128, 034108 (2008). JCPSA6 0021-9606 10.1063/1.2821021
48. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). PHRVAO 0031-899X 10.1103/PhysRev.140.A1133
49. M. P. Ljungberg, F. Ferrari, P. Koval, and Sánchez-Portal (unpublished).
50. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.1212
51. M. J. G. Peach and D. J. Tozer, J. Phys. Chem. A 116, 9783 (2012). JPCAFH 1089-5639 10.1021/jp308662x
52. M. J. G. Peach, M. J. Williamson, and D. J. Tozer, J. Chem. Theory Comput. 7, 3578 (2011). 1549-9618 10.1021/ct200651r
53. S. Sharifzadeh, P. Darancet, L. Kronik, and J. B. Neaton, J. Phys. Chem. Lett. 4, 2197 (2013). 1948-7185 10.1021/jz401069f
54. M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995).
55. M. Rohlfing and S. G. Louie, Phys. Rev. B 62, 4927 (2000). PRBMDO 0163-1829 10.1103/PhysRevB.62.4927
56. X. Ge, S. J. Binnie, D. Rocca, R. Gebauer, and S. Baroni, Comput. Phys. Commun. 185, 2080 (2014). CPHCBZ 0010-4655 10.1016/j.cpc.2014.03.005
57. H. Mori, Prog. Theor. Phys. 34, 399 (1965). PTPKAV 0033-068X 10.1143/PTP.34.399
58. M. H. Lee, Phys. Rev. Lett. 49, 1072 (1982). PRLTAO 0031-9007 10.1103/PhysRevLett.49.1072
59. Y. Saad, Iterative Methods for Sparse Linear Systems (Society for Industrial and Applied Mathematics, Philadelphia, 2003).
60. A. Greenbaum, Iterative Methods for Solving Linear Systems (Society for Industrial and Applied Mathematics, Philadelphia, 1997).
61. Numerical Analysis: Historical Developments in the 20th Century, edited by C. Brezinski and L. Wuytack (Elsevier, Amsterdam, 2001).
62. A. Mostafazadeh, J. Math. Phys. 43, 205 (2002). JMAPAQ 0022-2488 10.1063/1.1418246
63. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002). JMAPAQ 0022-2488 10.1063/1.1461427
64. R. Bauernschmitt and R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996). JCPSA6 0021-9606 10.1063/1.471637
65. F. Bruneval, J. Chem. Phys. 136, 194107 (2012). JCPSA6 0021-9606 10.1063/1.4718428
66. F. Bruneval, S. M. Hamed, and J. B. Neaton, J. Chem. Phys. 142, 244101 (2015). 10.1063/1.4922489
67. Experimental data obtained from the NIST Computational Chemistry Comparison and Benchmark DataBase at http://cccbdb.nist.gov, and the NIST webBook at http://webbook.nist.gov.
68. I. Vasiliev, S. Öʇüt, and J. R. Chelikowsky, Phys. Rev. Lett. 82, 1919 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.82.1919
69. W. R. Fredrickson and W. W. Watson, Phys. Rev. 30, 429 (1927). PHRVAO 0031-899X 10.1103/PhysRev.30.429
70. S. P. Sinha, Proc. Phys. Soc, Sect. A 62, 124 (1949). PPSAAM 0370-1298 10.1088/0370-1298/62/2/306
71. R. van Harrevelt, J. Chem. Phys. 126, 204313 (2007). 10.1063/1.2741551
72. F. Chen and C. Wu, J. Quant. Spectrosc. Radiat. Transfer 85, 195 (2004). JQSRAE 0022-4073 10.1016/S0022-4073(03)00225-5
73. J. C. Grossman, M. Rohlfing, L. Mitas, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 86, 472 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.472
74. M. L. Tiago and J. R. Chelikowsky, Solid State Commun. 136, 333 (2005). SSCOA4 0038-1098 10.1016/j.ssc.2005.08.012
75. P. Turchi, F. Ducastelle, and G. Treglia, J. Phys. C: Solid State Phys. 15, 2891 (1982). JPSOAW 0022-3719 10.1088/0022-3719/15/13/017
76. F. Bruneval, Ph.D. thesis, Ecole Polytechnique, 2005.
77. F. Sottile, Ph.D. thesis, Ecole Polytechnique, 2003.
78. P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959). PHRVAO 0031-899X 10.1103/PhysRev.115.1342