Dynamical mean-field theory for correlated electrons

Annalen der Physik (Leipzig)

Volumn 524, Issue 1, 2012, Pages 1-19

  Vollhardt, D ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Correlated lattice fermions; dynamical mean field theory

Indexed keywords

CORRELATED ELECTRONS; CORRELATED MATERIALS; CORRELATION MODELS; DISCONTINUOUS TRANSITION; DYNAMICAL MEAN-FIELD THEORY; ELECTRONIC CORRELATION; LATTICE DIMENSIONS; MANY-BODY APPROACH; QUANTUM MANY-BODY SYSTEMS;

QUANTUM THEORY;

MEAN FIELD THEORY;

EID: 84255214267     PISSN: 00033804     EISSN: 15213889     Source Type: Journal    
DOI: 10.1002/andp.201100250     Document Type: Review

References (162)

1. J.H. de Boer, and, E.J.W. Verwey, Proc. Phys. Soc. 49(4S), 59 (1937).
2. N.F. Mott, and, R. Peierls, Proc. Phys. Soc. Lond. A 49, 72 (1937).
3. N. Grewe, and, F. Steglich, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 14, edited by K. A. Gschneidner Jr. and L. Eyring (North Holland, Amsterdam, 1991) p. 343.
4. J.R. Schrieffer, Handbook of High-Temperature Superconductivity, edited by J. R. Schrieffer (Springer, Berlin, 2007).
5. E. Dagotto, Nanoscale Phase Separation and Collossal Magnetoresistance (Springer, Berlin, 2002).
6. M. Imada, A. Fujimori, and, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).
7. H. v. Löhneysen, A. Rosch, M. Vojta, and, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007).
8. Y. Tokura, Phys. Today, Juli 2003, p. 50.
9. M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
10. J. Hubbard, Proc. Roy. Soc. London A276, 238 (1963).
11. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).
12. E. Lieb, and, F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).
13. P. Fulde, Electron Correlations in Molecules and Solids (Springer, Berlin, 1995).
14. D. Vollhardt, in: Lectures on the Physics of Strongly Correlated Systems XIV, AIP Conference Proceedings, Vol. 1297, edited by by A. Avella and F. Mancini (American Institute of Physics, Melville, 2010) p. 339; arXiv:1004.5069v3.
15. H.E. Stanley, in: Phase Transitions and Critical Phenomena, Vol. 3, edited by C. Domb and M. S. Green (Academic Press, London, 1974) p. 485.
16. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
17. E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969).
18. R.P. Feynman, Statistical Physics (Benjamin, Reading, 1972).
19. V.R. Pandharipande, and, R.B. Wiringa, Rev. Mod. Phys. 51, 821 (1979).
20. J. Bardeen, L.N. Cooper, and, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).
21. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
22. For a brief review of variational wave functions for correlated electron systems see D. Vollhardt, in: Interacting Electrons in Reduced Dimensions, edited by D. Baeriswyl and D. Campbell (Plenum Press, New York, 1989) p. 107.
23. D. Vollhardt, in: Correlated Electron Systems, edited by V. J. Emery (World Scientific, Singapore, 1993) p. 57; http://www.physik.uni-augsburg.de/ theo3/Research/research-jerusalem.vollha.en.shtml.
24. M.C. Gutzwiller, Phys. Rev. 137, A1726 (1965).
25. W.F. Brinkman, and, T.M. Rice, Phys. Rev. B 2, 4302 (1970).
26. T.M. Rice, and, W.F. Brinkman, in: Alloys, Magnets, and Superconductors, edited by R. E. Mills, E. Ascher, and R. Jaffee (McGraw-Hill, New York, 1971) p. 593.
27. P.W. Anderson, and, W.F. Brinkman, in: The Physics of Liquid and Solid Helium, Part II, edited by K. H. Bennemann and J. B. Ketterson (Wiley, New York, 1978) p. 177.
28. K. Levin, and, O.T. Valls, Phys. Rep. 98, 1 (1983).
29. B. Castaing, and, P. Nozìres, J. Phys. (Paris) 40, 257 (1979).
30. D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984).
31. D. Vollhardt, P. Wölfle, and, P.W. Anderson, Phys. Rev. B 35, 6703 (1987).
32. W. Metzner, and, D. Vollhardt, Phys. Rev. Lett. 59, 121 (1987).
33. W. Metzner, and, D. Vollhardt, Phys. Rev. B 37, 7382 (1988).
34. M. Kollar, and, D. Vollhardt, Phys. Rev. B 65, 155121 (2002).
35. E.H. Lieb, and, D. Mattis, Phys. Rev. 125, 164 (1962).
36. F. Gebhard, and, D. Vollhardt, Phys. Rev. Lett. 59, 1472 (1987).
37. F. Gebhard, and, D. Vollhardt, Phys. Rev. B 38, 6911 (1988).
38. F.D.M. Haldane, Phys. Rev. Lett. 60, 635 (1988).
39. B.S. Shastry, Phys. Rev. Lett. 60, 639 (1988).
40. P.W. Anderson, Mater. Res. Bull. 8, 153 (1973).
41. P. Fazekas, and, P.W. Anderson, Philos. Mag. 30, 432 (1974).
42. P.W. Anderson, G. Baskeran, Z. Zou, and, T. Hsu, Phys. Rev. Lett. 58, 2790 (1987).
43. W. Metzner, and, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).
44. W. Metzner, Z. Phys. B 77, 253 (1989).
45. P.G.J. van Dongen, F. Gebhard, and, D. Vollhardt, Z. Phys. 76, 199 (1989).
46. U. Wolff, Nucl. Phys. B 225, 391 (1983).
47. G. Kotliar, and, A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986).
48. D. Vollhardt, P.G.J. van Dongen, F. Gebhard, and, W. Metzner, Mod. Phys. Lett. B 4, 499 (1990).
49. F. Gebhard, Phys. Rev. B 41, 9452 (1990).
50. J. Bünemann, F. Gebhard, and, W. Weber, Found. Phys. 30, 2011 (2000).
51. W. Weber, J. Bünemann, and, F. Gebhard, in: Bandferromagnetism, edited by K. Baberschke, M. Donath and W. Nolting, (Springer, Berlin, 2001) p. 9.
52. W. Metzner, and, D. Vollhardt, Phys. Rev. B 39, 4462 (1989).
53. E. Müller-Hartmann, Z. Phys. B 74, 507 (1989).
54. E. Müller-Hartmann, Z. Phys. B 76, 211 (1989).
55. H. Schweitzer, and, G. Czycholl, Solid State Commun. 69, 171 (1989).
56. U. Brandt, and, C. Mielsch, Z. Phys. B 75, 365 (1989).
57. P.G.J. van Dongen, and, D. Vollhardt, Phys. Rev. Lett. 65, 1663 (1990).
58. W. Metzner, P. Schmit, and, D. Vollhardt, Phys. Rev. B 45, 2237 (1992).
59. R. Strack, and, D. Vollhardt, Phys. Rev. B 46, 13852 (1992).
60. V. Janiš, Z. Phys. B 83, 227 (1991).
61. V. Janiš, and, D. Vollhardt, Int. J. Mod. Phys. B 6, 731 (1992).
62. R. Vlaming, and, D. Vollhardt, Phys. Rev. B 45, 4637 (1992).
63. A. Georges, and, G. Kotliar, Phys. Rev. B 45, 6479 (1992).
64. M. Jarrell, Phys. Rev. Lett. 69, 168 (1992).
65. A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993).
66. J.E. Hirsch, and, R.M. Fye, Phys. Rev. Lett. 56, 2521 (1986).
67. A. Georges, G. Kotliar, W. Krauth, and, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
68. G. Kotliar, and, D. Vollhardt, Phys. Today 3, 53 (2004).
69. V. Janiš, and, D. Vollhardt, Phys. Rev. B 46, 15712 (1992).
70. R. Vlaming, G.S. Uhrig, and, D. Vollhardt, J. Phys., Condens. Matter 4, 7773 (1992).
71. R. Vlaming, and, G.S. Uhrig, J. Phys., Condens. Matter 5, 2561 (1993).
72. X.Y. Zhang, M.J. Rozenberg, and, G. Kotliar, Phys. Rev. Lett. 70, 1666 (1993).
73. J.K. Freericks, and, V. Zlatić, Rev. Mod. Phys. 75, 1333 (2003).
74. M.J. Rozenberg, X.Y. Zhang, and, G. Kotliar, Phys. Rev. Lett. 69, 1236 (1992).
75. A. Georges, and, W. Krauth, Phys. Rev. Lett. 69, 1240 (1992).
76. Th. Maier, M. Jarrell, Th. Pruschke, and, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005).
77. E. Gull, et al., Rev. Mod. Phys. 83, 349 (2011).
78. R. Bulla, Phys. Rev. Lett. 83, 136 (1999).
79. W. Hofstetter, Phys. Rev. Lett. 85, 1508 (2000)
80. R. Bulla, T.A. Costi, and, Th. Pruschke, Rev. Mod. Phys. 80, 395 (2008).
81. M. Caffarel, and, W. Krauth, Phys. Rev. Lett. 72, 1545 (1994).
82. Q. Si, M.J. Rozenberg, G. Kotliar, and, A.E. Ruckenstein, Phys. Rev. Lett. 72, 2761 (1994).
83. M.J. Rozenberg, G. Moeller, and, G. Kotliar, Mod. Phys. Lett. B 8, 535 (1994).
84. Th. Pruschke, M. Jarrell, and, J.K. Freericks, Adv. Phys. 44, 187 (1995).
85. A. Georges, in: Lectures on the Physics of Highly Correlated Electron Systems VIII, edited by A. Avella and F. Mancini, AIP Conference Proceedings, Vol. 715 (American Institute of Physics, Melville, 2004) p. 3.
86. N.F. Mott, Rev. Mod. Phys. 40, 677 (1968).
87. N.F. Mott, Metal-Insulator Transitions, 2nd edition (Taylor and Francis, London, 1990).
88. F. Gebhard, The Mott Metal-Insulator Transition (Springer, Berlin, 1997).
89. D.B. McWhan, et al., Phys. Rev. B 2, 1920 (1973).
90. J. Hubbard, Proc. R. Soc. Lond. A 281, 401 (1964).
91. N. Blümer, Metal-Insulator Transition and Optical Conductivity in High Dimensions (Shaker Verlag, Aachen, 2003).
92. D. Vollhardt, et al., J. Phys. Soc. Jpn. 74, 136 (2005).
93. M.J. Rozenberg, R. Chitra, and, G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).
94. J. Joo, and, V. Oudovenko, Phys. Rev. B 64, 193102 (2001).
95. R. Bulla, T.A. Costi, and, D. Vollhardt, Phys. Rev. B 64, 045103 (2001).
96. D. Vollhardt, and, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990).
97. C. Enss, and, S. Hunklinger, Low-Temperature Physics (Springer, Berlin, 2010).
98. H. Park, K. Haule, and, G. Kotliar, Phys. Rev. Lett. 101, 186403 (2008).
99. K. Byczuk, M. Ulmke, and, D. Vollhardt, Phys. Rev. Lett. 90, 196403 (2003).
100. K. Byczuk, W. Hofstetter, and, D. Vollhardt, Phys. Rev. B 69, 045112 (2004).
101. K. Byczuk, W. Hofstetter, and, D. Vollhardt, Phys. Rev. Lett. 94, 056404 (2005).
102. K. Byczuk, W. Hofstetter, and, D. Vollhardt, in: Fifty Years of Anderson Localization, edited by E. Abrahams (World Scientific, Singapore, 2010) p. 473; reprinted in Int. J. Mod. Phys. B 24, 1727 (2010).
103. P. Hohenberg, and, W. Kohn, Phys. Rev. 136B, 864 (1964).
104. W. Kohn, and, L.J. Sham, Phys. Rev. 140, A1133 (1965).
105. R.O. Jones, and, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).
106. V.I. Anisimov, J. Zaanen, and, O.K. Andersen, Phys. Rev. B 44, 943 (1991).
107. V.I. Anisimov, F. Aryasetiawan, and, A.I. Lichtenstein, J. Phys., Condens. Matter 9, 767 (1997).
108. V.I. Anisimov, et al., J. Phys., Condens. Matter. 9, 7359 (1997).
109. A.I. Lichtenstein, and, M.I. Katsnelson, Phys. Rev. B 57, 6884 (1998).
110. I.A. Nekrasov, et al., Eur. Phys. J. B 18, 55 (2000).
111. K. Held, et al., Int. J. Mod. Phys. B 15, 2611 (2001).
112. A.I. Lichtenstein, M.I. Katsnelson, and, G. Kotliar, in: Electron Correlations and Materials Properties, edited by A. Gonis, N. Kioussis, and M. Ciftan (Kluwer Academic/Plenum, New York, 2002) p. 428.
113. K. Held, et al., Psi-k Newsletter 56, 65 (2003); reprinted in Phys. Status Solidi B 243, 2599 (2006).
114. G. Kotliar, et al., Rev. Mod. Phys. 78, 865 (2006).
115. K. Held, Adv. Phys. 56, 829 (2007).
116. M.I. Katsnelson, et al., Rev. Mod. Phys. 80, 315 (2008).
117. J. Kuneš, et al., Eur. Phys. J. Special Topics 180, 5 (2010).
118. S. Biermann, F. Aryasetiawan, and, A. Georges, Phys. Rev. Lett. 90, 086402 (2003).
119. J. Minár, et al., Phys. Rev. B 72, 45125 (2005).
120. A. Fujimori, et al., Phys. Rev. Lett. 69, 1796 (1992).
121. A. Sekiyama, et al., Phys. Rev. Lett. 93, 156402 (2004).
122. D. Schrupp, et al., Europhys. Lett. 70, 789 (2005).
123. T.C. Koethe, et al., Phys. Rev. Lett. 97, 116402 (2006).
124. E. Pavarini, et al., Phys. Rev. Lett. 92, 176403 (2004).
125. I.A. Nekrasov, et al., Phys. Rev. B 72, 155106 (2005).
126. I.H. Inoue, et al., Physica C 235-240, 1007 (1994).
127. I.A. Nekrasov, et al., Phys. Rev. B 73, 155112 (2006).
128. T. Yoshida, et al., Phys. Rev. Lett. 95, 146404 (2005).
129. A. Lanzara, et al., Nature 412, 510 (2001).
130. Z.-X. Shen, A. Lanzara, S. Ishihara, and, N. Nagaosa, Philos. Mag. B 82, 1349 (2002).
131. H. He, et al., Phys. Rev. Lett. 86, 1610 (2001).
132. J. Hwang, T. Timusk, and, G.D. Gu, Nature 427, 714 (2004).
133. M. Hengsberger, et al., Phys. Rev. Lett. 83, 592 (1999).
134. E. Rotenberg, J. Schaefer, and, S.D. Kevan, Phys. Rev. Lett. 84, 2925 (2000).
135. J. Schäfer, et al., Phys. Rev. Lett. 92, 097205 (2004).
136. K. Byczuk, et al., Nature Phys. 3, 168 (2007).
137. A. Toschi, M. Capone, C. Castellani, and, K. Held, Phys. Rev. Lett. 102, 076402 (2009).
138. C. Raas, P. Grete, and, G.S. Uhrig, Phys. Rev. Lett. 102, 076406 (2009).
139. A. Hofmann, et al., Phys. Rev. Lett. 102, 187204 (2009).
140. M. Potthoff, and, W. Nolting, Phys. Rev. B 59, 2549 (1999).
141. J.K. Freericks, Transport in Multilayered Nanostructures-The Dynamical Mean-field Approach (Imperial College Press, London, 2006).
142. M. Takizawa, et al., Phys. Rev. Lett. 97, 057601 (2006).
143. L. Chen, and, J.K. Freericks, Phys. Rev. B 75, 1251141 (2007).
144. K. Byczuk, in: Condensed Matter Physics in the Prime of the 21st Century: Phenomena, Materials, Ideas, Methods, edited by J. Jedrzejewski (World Scientific, Singapore, 2008) p. 1.
145. R.W. Helmes, T.A. Costi, and, A. Rosch, Phys. Rev. Lett. 100, 056403 (2008).
146. D. Jaksch, et al., Phys. Rev. Lett. 81, 3108 (1998).
147. W. Hofstetter, et al., Phys. Rev. Lett. 89, 220407 (2002).
148. M. Greiner, et al., Nature 415, 39 (2002).
149. A. Rapp, G. Zarand, C. Honerkamp, and, W. Hofstetter, Phys. Rev. Lett. 98, 160405 (2007).
150. M. Snoek, et al., New J. Phys. 10, 093008 (2008).
151. R. Jördens, et al., Nature 455, 204 (2008).
152. U. Schneider, et al., Science 322, 1520 (2008).
153. I. Bloch, J. Dalibard, and, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
154. V. Turkowski, and, J.K. Freericks, Phys. Rev. B 71, 085104 (2005).
155. J.K. Freericks, V.M. Turkowski, and, V. Zlatić, Phys. Rev. Lett. 97, 266408 (2006).
156. J.K. Freericks, Phys. Rev. B 77, 075109 (2008).
157. N. Tsuji, T. Oka, and, H. Aoki, Phys. Rev. B 78, 235124 (2008).
158. M. Eckstein, and, M. Kollar, Phys. Rev. Lett. 100, 120404 (2008).
159. M. Eckstein, and, M. Kollar, Phys. Rev. B 78, 205119 (2008).
160. J.K. Freericks, H.R. Krishnamurthy, and, Th. Pruschke, Phys. Rev. Lett. 102, 136401 (2009).
161. M. Eckstein, M. Kollar, and, P. Werner, Phys. Rev. Lett. 103, 056403 (2009).
162. M. Eckstein, and, P. Werner, Phys. Rev. B 82, 115115 (2010).