The density matrix renormalization group for ab initio quantum chemistry

European Physical Journal D

Volumn 68, Issue 9, 2014, Pages

  Wouters, Sebastian ^a   Van Neck, Dimitri ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ONE DIMENSIONAL; QUANTUM THEORY; STATISTICAL MECHANICS;

AB INITIO QUANTUM CHEMISTRY; DECAYING CORRELATIONS; DENSITY MATRIX RENORMALIZATION GROUP; FULL CONFIGURATION INTERACTION; LOW-RANK DECOMPOSITION; MATRIX PRODUCT STATE; NUMERICAL CONVERGENCE; ONE-DIMENSIONAL SYSTEMS;

QUANTUM CHEMISTRY;

EID: 84907291976     PISSN: 14346060     EISSN: 14346079     Source Type: Journal    
DOI: 10.1140/epjd/e2014-50500-1     Document Type: Article

References (175)

1. D.R. Hartree, Math. Proc. Cambridge Philos. Soc. 24, 89 (1928)
2. J.C. Slater, Phys. Rev. 32, 339 (1928)
3. V. Fock, Z. Phys. 61, 126 (1926)
4. T. Helgaker, P. Jorgensen, J. Olsen, Molecular electronic-structure theory, 1st edn. (Wiley, New-York, 2000)
5. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
6. W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)
7. R.M. Dickson, A.D. Becke, J. Chem. Phys. 123, 111101 (2005)
8. C. Moller, M.S. Plesset, Phys. Rev. 46, 618 (1934)
9. J.C. Slater, Phys. Rev. 34, 1293 (1929)
10. E.U. Condon, Phys. Rev. 36, 1121 (1930)
11. F. Coester, Nucl. Phys. 7, 421 (1958)
12. F. Coester, H. Kümmel, Nucl. Phys. 17, 477 (1960)
13. J. ČíŽek, J. Chem. Phys. 45, 4256 (1966)
14. B.O. Roos, Int. J. Quantum Chem. 18, 175 (1980)
15. B.O. Roos, P.R. Taylor, P.E.M. Siegbahn, Chem. Phys. 48, 157 (1980)
16. P.E.M. Siegbahn, J. Almlöf, A. Heiberg, B.O. Roos, J. Chem. Phys. 74, 2384 (1981)
17. P.-Å. Malmqvist, A. Rendell, B.O. Roos, J. Phys. Chem. 94, 5477 (1990)
18. K. Andersson, P.-Å. Malmqvist, B.O. Roos, J. Chem. Phys. 96, 1218 (1992)
19. R.J. Buenker, S.D. Peyerimhoff, Theor. Chim. Acta 35, 33 (1974)
20. H.-J. Werner, E.-A. Reinsch, J. Chem. Phys. 76, 3144 (1982)
21. P.E.M. Siegbahn, J. Chem. Phys. 70, 5391 (1979)
22. P.E.M. Siegbahn, J. Chem. Phys. 72, 1647 (1980)
23. B.R. Brooks, H.F. Schaefer, J. Chem. Phys. 70, 5092 (1979)
24. N. Oliphant, L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)
25. L.Z. Stolarczyk, Chem. Phys. Lett. 217, 1 (1994)
26. T. Yanai, G.K.-L. Chan, J. Chem. Phys. 124, 194106 (2006)
27. S.R. White, R.L. Martin, J. Chem. Phys. 110, 4127 (1999)
28. J.F. Cornwell, in Group theory in physics, 1st edn. (Academic Press Inc., Ltd., London, 1984), Vols. 1 and 2
29. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)
30. S.R. White, Phys. Rev. B 48, 10345 (1993)
31. S. Östlund, S. Rommer, Phys. Rev. Lett. 75, 3537 (1995)
32. S. Rommer, S. Östlund, Phys. Rev. B 55, 2164 (1997)
33. M.B. Hastings, J. Stat. Mech.: Theor. Exp. 2007, P08024 (2007)
34. T. Nishino, Origin of Matrix Product State in Statistical Mechanics, in International Workshop on Density Matrix Renormalization Group and Other Advances in Numerical Renormalization Group Methods, August 23-September 3, 2010
35. H.A. Kramers, G.H. Wannier, Phys. Rev. 60, 263 (1941)
36. R.J. Baxter, J. Math. Phys. 9, 650 (1968)
37. M.P. Nightingale, H.W.J. Blöte, Phys. Rev. B 33, 659 (1986)
38. I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)
39. M. Fannes, B. Nachtergaele, R.F. Werner, Europhys. Lett. 10, 633 (1989)
40. M. Fannes, B. Nachtergaele, R.F. Werner, Commun. Math. Phys. 144, 443 (1992)
41. I. Oseledets, SIAM J. Sci. Comput. 33, 2295 (2011)
42. D.V. Savostyanov, S.V. Dolgov, J.M. Werner, I. Kuprov, Phys. Rev. B 90, 085139 (2014)
43. S. Tomonaga, Prog. Theor. Phys. 1, 27 (1946)
44. J. Schwinger, Phys. Rev. 73, 416 (1948)
45. J. Schwinger, Phys. Rev. 74, 1439 (1948)
46. R.P. Feynman, Phys. Rev. 76, 769 (1949)
47. R.P. Feynman, Phys. Rev. 76, 749 (1949)
48. K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
49. S.R. White, R.M. Noack, Phys. Rev. Lett. 68, 3487 (1992)
50. J. von Neumann, Mathematisch-Physikalische Klasse 1927, 273 (1927)
51. M.B. Plenio, J. Eisert, J. Dreiβig, M. Cramer, Phys. Rev. Lett. 94, 060503 (2005)
52. J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010)
53. K. Van Acoleyen, M. Mariën, F. Verstraete, Phys. Rev. Lett. 111, 170501 (2013)
54. G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
55. G. Evenbly, G. Vidal, J. Stat. Phys. 145, 891 (2011)
56. E.M. Stoudenmire, S.R. White, Ann. Rev. Condens. Matter Phys. 3, 111 (2012)
57. F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405 (2010)
58. F. Verstraete, J.I. Cirac, arXiv:cond-mat/0407066 (2004)
59. G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)
60. F. Verstraete, D. Porras, J.I. Cirac, Phys. Rev. Lett. 93, 227205 (2004)
61. Y.-Y. Shi, L.-M. Duan, G. Vidal, Phys. Rev. A 74, 022320 (2006)
62. A.J. Ferris, Phys. Rev. B 87, 125139 (2013)
63. V. Murg, F. Verstraete, Ö. Legeza, R.M. Noack, Phys. Rev. B 82, 205105 (2010)
64. V. Murg, F. Verstraete, R. Schneider, P.R. Nagy, Ö. Legeza, arXiv:1403.0981 (2014)
65. T. Xiang, Phys. Rev. B 53, R10445 (1996)
66. S. Daul, I. Ciofini, C. Daul, S.R. White, Int. J. Quantum Chem. 79, 331 (2000)
67. A.O. Mitrushchenkov, G. Fano, F. Ortolani, R. Linguerri, P. Palmieri, J. Chem. Phys. 115, 6815 (2001)
68. G.K.-L. Chan, M. Head-Gordon, J. Chem. Phys. 116, 4462 (2002)
69. Ö. Legeza, J. Röder, B.A. Hess, Phys. Rev. B 67, 125114 (2003)
70. G.K.-L. Chan, M. Head-Gordon, J. Chem. Phys. 118, 8551 (2003)
71. Ö. Legeza, J. Röder, B.A. Hess, Mol. Phys. 101, 2019 (2003)
72. A.O. Mitrushchenkov, R. Linguerri, P. Palmieri, G. Fano, J. Chem. Phys. 119, 4148 (2003)
73. Ö. Legeza, J. Sólyom, Phys. Rev. B 68, 195116 (2003)
74. G.K.-L. Chan, J. Chem. Phys. 120, 3172 (2004)
75. G.K.-L. Chan, M. Kállay, J. Gauss, J. Chem. Phys. 121, 6110 (2004)
76. Ö. Legeza, J. Sólyom, Phys. Rev. B 70, 205118 (2004)
77. G. Moritz, B.A. Hess, M. Reiher, J. Chem. Phys. 122, 024107 (2005)
78. G.K.-L. Chan, T. Van Voorhis, J. Chem. Phys. 122, 204101 (2005)
79. G. Moritz, A. Wolf, M. Reiher, J. Chem. Phys. 123, 184105 (2005)
80. G. Moritz, M. Reiher, J. Chem. Phys. 124, 034103 (2006)
81. J. Hachmann, W. Cardoen, G.K.-L. Chan, J. Chem. Phys. 125, 144101 (2006)
82. J. Rissler, R.M. Noack, S.R. White, Chem. Phys. 323, 519 (2006)
83. G. Moritz, M. Reiher, J. Chem. Phys. 126, 244109 (2007)
84. J.J. Dorando, J. Hachmann, G.K.-L. Chan, J. Chem. Phys. 127, 084109 (2007)
85. J. Hachmann, J.J. Dorando, M. Avilés, G.K.-L. Chan, J. Chem. Phys. 127, 134309 (2007)
86. K.H. Marti, I.M. Ondík, G. Moritz, M. Reiher, J. Chem. Phys. 128, 014104 (2008)
87. D. Zgid, M. Nooijen, J. Chem. Phys. 128, 014107 (2008)
88. D. Zgid, M. Nooijen, J. Chem. Phys. 128, 144115 (2008)
89. D. Zgid, M. Nooijen, J. Chem. Phys. 128, 144116 (2008)
90. D. Ghosh, J. Hachmann, T. Yanai, G.K.-L. Chan, J. Chem. Phys. 128, 144117 (2008)
91. G.K.-L. Chan, Phys. Chem. Chem. Phys. 10, 3454 (2008)
92. T. Yanai, Y. Kurashige, D. Ghosh, G.K.-L. Chan, Int. J. Quantum Chem. 109, 2178 (2009)
93. J.J. Dorando, J. Hachmann, G.K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)
94. Y. Kurashige, T. Yanai, J. Chem. Phys. 130, 234114 (2009)
95. T. Yanai, Y. Kurashige, E. Neuscamman, G.K.-L. Chan, J. Chem. Phys. 132, 024105 (2010)
96. E. Neuscamman, T. Yanai, G.K.-L. Chan, J. Chem. Phys. 132, 024106 (2010)
97. K.H. Marti, M. Reiher, Mol. Phys. 108, 501 (2010)
98. H.-G. Luo, M.-P. Qin, T. Xiang, Phys. Rev. B 81, 235129 (2010)
99. W. Mizukami, Y. Kurashige, T. Yanai, J. Chem. Phys. 133, 091101 (2010)
100. K.H. Marti, B. Bauer, M. Reiher, M. Troyer, F. Verstraete, New J. Phys. 12, 103008 (2010)
101. K.H. Marti, M. Reiher, Phys. Chem. Chem. Phys. 13, 6750 (2011)
102. G. Barcza, Ö. Legeza, K.H. Marti, M. Reiher, Phys. Rev. A 83, 012508 (2011)
103. K. Boguslawski, K.H. Marti, M. Reiher, J. Chem. Phys. 134, 224101 (2011)
104. Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)
105. A.O. Mitrushchenkov, G. Fano, R. Linguerri, P. Palmieri, Int. J. Quantum Chem. 112, 1606 (2012)
106. S. Sharma, G.K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)
107. S. Wouters, P.A. Limacher, D. Van Neck, P.W. Ayers, J. Chem. Phys. 136, 134110 (2012)
108. K. Boguslawski, K.H. Marti, Ö. Legeza, M. Reiher, J. Chem. Theor. Comput. 8, 1970 (2012)
109. T. Yanai, Y. Kurashige, E. Neuscamman, G.K.-L. Chan, Phys. Chem. Chem. Phys. 14, 7809 (2012)
110. K. Boguslawski, P. Tecmer, Ö. Legeza, M. Reiher, J. Phys. Chem. Lett. 3, 3129 (2012)
111. W. Mizukami, Y. Kurashige, T. Yanai, J. Chem. Theor. Comput. 9, 401 (2013)
112. N. Nakatani, G.K.-L. Chan, J. Chem. Phys. 138, 134113 (2013)
113. K. Boguslawski, P. Tecmer, G. Barcza, Ö. Legeza, M. Reiher, J. Chem. Theor. Comput. 9, 2959 (2013)
114. Y. Kurashige, G.K.-L. Chan, T. Yanai, Nat. Chem. 5, 660 (2013)
115. Y. Ma, H. Ma, J. Chem. Phys. 138, 224105 (2013)
116. M. Saitow, Y. Kurashige, T. Yanai, J. Chem. Phys. 139, 044118 (2013)
117. F. Liu, Y. Kurashige, T. Yanai, K. Morokuma, J. Chem. Theor. Comput. 9, 4462 (2013)
118. P. Tecmer, K. Boguslawski, Ö. Legeza, M. Reiher, Phys. Chem. Chem. Phys. 16, 719 (2014)
119. N. Nakatani, S. Wouters, D. Van Neck, G.K.-L. Chan, J. Chem. Phys. 140, 024108 (2014)
120. S. Knecht, Ö. Legeza, M. Reiher, J. Chem. Phys. 140, 041101 (2014)
121. S. Wouters, W. Poelmans, P.W. Ayers, D. Van Neck, Comput. Phys. Commun. 185, 1501 (2014)
122. T.V. Harris, Y. Kurashige, T. Yanai, K. Morokuma, J. Chem. Phys. 140, 054303 (2014)
123. M. Mottet, P. Tecmer, K. Boguslawski, Ö. Legeza, M. Reiher, Phys. Chem. Chem. Phys. 16, 8872 (2014)
124. T.N. Lan, Y. Kurashige, T. Yanai, J. Chem. Theor. Comput. 10, 1953 (2014)
125. S. Sharma, T. Yanai, G.H. Booth, C.J. Umrigar, G.K.-L. Chan, J. Chem. Phys. 140, 104112 (2014)
126. Y. Kurashige, M. Saitow, J. Chalupsky, T. Yanai, Phys. Chem. Chem. Phys. 16, 11988 (2014)
127. S. Wouters, T. Bogaerts, P. Van Der Voort, V. Van Speybroeck, D. Van Neck, J. Chem. Phys. 140, 241103 (2014)
128. E. Fertitta, B. Paulus, G. Barcza, Ö. Legeza, arXiv:1406.7038 (2014)
129. G.K.-L. Chan, J.J. Dorando, D. Ghosh, J. Hachmann, E. Neuscamman, H. Wang, T. Yanai, Frontiers in Quantum Systems in Chemistry and Physics, in Progress in Theoretical Chemistry and Physics, edited by S. Wilson, P.J. Grout, J. Maruani, G. Delgado-Barrio, P. Piecuch (Springer, 2008), Vol. 18, pp. 49-65
130. G.K.-L. Chan, D. Zgid, The Density Matrix Renormalization Group in Quantum Chemistry, in Annual Reports in Computational Chemistry (Elsevier, 2009), Vol. 5, Chap. 7, pp. 149-162
131. K.H. Marti, M. Reiher, Z. Phys. Chem. 224, 583 (2010)
132. G.K.-L. Chan, S. Sharma, Ann. Rev. Phys. Chem. 62, 465 (2011)
133. G.K.-L. Chan, WIREs Comput. Mol. Sci. 2, 907 (2012)
134. Y. Kurashige, Mol. Phys. 112, 1485 (2014)
135. S.F. Keller, M. Reiher, Chimia 68, 200 (2014)
136. C. Lanczos, J. Res. Nat. Bureau Stand. 45, 255 (1950)
137. E.R. Davidson, J. Comput. Phys. 17, 87 (1975)
138. P. Jordan, E. Wigner, Z. Phys. 47, 631 (1928)
139. S. Wouters, Ph.D. thesis, Ghent University, 2014
140. C. Edmiston, K. Ruedenberg, Rev. Mod. Phys. 35, 457 (1963)
141. Ö. Legeza, G. Fáth, Phys. Rev. B 53, 14349 (1996)
142. G.K.-L. Chan, P.W. Ayers, E.S. Croot III, J. Stat. Phys. 109, 289 (2002)
143. S.R. White, Phys. Rev. B 72, 180403 (2005)
144. S.R. White, Phys. Rev. Lett. 77, 3633 (1996)
145. B.C. Carlson, J.M. Keller, Phys. Rev. 105, 102 (1957)
146. J. Pipek, P.G. Mezey, J. Chem. Phys. 90, 4916 (1989)
147. A.O. Mitrushchenkov, G. Fano, R. Linguerri, P. Palmieri, arXiv:cond-mat/0306058 (2003)
148. J. Hubbard, Proc. Roy. Soc. Lond. Ser. A 276, 238 (1963)
149. K. Hallberg, Density Matrix Renormalization, in Theoretical Methods for Strongly Correlated Electrons, edited by D. Sénéchal, A.-M. Tremblay, C. Bourbonnais, CRM Series in Mathematical Physics (Springer, New York, 2004), Chap. 1, pp. 3-37
150. B. Pirvu, J. Haegeman, F. Verstraete, Phys. Rev. B 85, 035130 (2012)
151. J. Haegeman, B. Pirvu, D.J. Weir, J.I. Cirac, T.J. Osborne, H. Verschelde, F. Verstraete, Phys. Rev. B 85, 100408 (2012)
152. S. Wouters, N. Nakatani, D. Van Neck, G.K.-L. Chan, Phys. Rev. B 88, 075122 (2013)
153. J. Haegeman, T.J. Osborne, F. Verstraete, Phys. Rev. B 88, 075133 (2013)
154. J. Haegeman, J.I. Cirac, T.J. Osborne, I. PiŽorn, H. Verschelde, F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)
155. J.M. Kinder, C.C. Ralph, G.K.-L. Chan, Quantum Information and Computation for Chemistry, in Advances in Chemical Physics, edited by S. Kais (John Wiley & Sons, 2014), Vol. 154, Chap. 7, pp. 179-192
156. F. Mezzacapo, N. Schuch, M. Boninsegni, J.I. Cirac, New J. Phys. 11, 083026 (2009)
157. H. Weyl, Gruppentheorie und Quantenmechanik. (Hirzel, Leipzig, 1928)
158. E. Wigner, Ann. Math. 40, 149 (1939)
159. G. Sierra, T. Nishino, Nucl. Phys. B 495, 505 (1997)
160. I.P. McCulloch, M. Gulácsi, Austr. J. Phys. 53, 597 (2000)
161. I.P. McCulloch, M. Gulácsi, Philos. Mag. Lett. 81, 447 (2001)
162. I.P. McCulloch, M. Gulácsi, Europhys. Lett. 57, 852 (2002)
163. I.P. McCulloch, J. Stat. Mech.: Theory Exp. 2007, P10014 (2007)
164. S. Singh, H.-Q. Zhou, G. Vidal, New J. Phys. 12, 033029 (2010)
165. S. Singh, R.N.C. Pfeifer, G. Vidal, Phys. Rev. A 82, 050301 (2010)
166. S. Singh, G. Vidal, Phys. Rev. B 86, 195114 (2012)
167. S. Pittel, N. Sandulescu, Phys. Rev. C 73, 014301 (2006)
168. J. Rotureau, N. Michel, W. Nazarewicz, M. Płoszajczak, J. Dukelsky, Phys. Rev. Lett. 97, 110603 (2006)
169. B. Thakur, S. Pittel, N. Sandulescu, Phys. Rev. C 78, 041303 (2008)
170. A. Weichselbaum, Ann. Phys. 327, 2972 (2012)
171. Ö. Legeza, J. Sólyom, Phys. Rev. B 56, 14449 (1997)
172. W.H. Dickhoff, D. Van Neck, Many-body theory exposed!, 2nd edn. (World Scientific, 2008)
173. S. Sharma, G.K.-L. Chan, Block code for DMRG (2012), http://www.princeton.edu/chemistry/chan/software/dmrg/
174. S. Wouters, CheMPS2: a spin-adapted implementation of DMRG for ab initio quantum chemistry (2014), https://github.com/SebWouters/CheMPS2
175. E.M. Stoudenmire, S.R. White, Phys. Rev. B 87, 155137 (2013)