Abstract
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
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Notes
- 1.
The coordination number Z is determined by the dimension d and the lattice structure. Already in d = 3 the coordination number can be quite large, e.g., Z = 6 for a simple cubic lattice, Z = 8 for a bcc-lattice and Z = 12 for an fcc-lattice, making its inverse, 1 ∕ Z, rather small. It is then natural to consider the limit Z → ∞ to simplify the problem. For a hypercubic lattice, obtained by generalizing the simple cubic lattice in d = 3 to arbitrary dimensions, one has Z = 2d. The limit d → ∞ is then equivalent to Z → ∞. Several standard approximation schemes which are commonly used to explain experimental results in dimension d = 3 are exact only in d, Z = ∞ [9].
- 2.
In the following we set the Planck constant \(\hslash \), the Boltzmann constant k B, and the lattice constant a equal to unity.
- 3.
Here a “path” is any sequence of lines in a diagram; they are “separate” when they have no lines in common.
- 4.
In d = ∞ limit the notion of a Fermi surface of a lattice system is complicated by the fact that the dispersion ε k is not a simple smooth function.
- 5.
- 6.
- 7.
In principle, any one of the local functions \({\mathcal{G}}_{\sigma }(i{\omega }_{n})\), \({\Sigma }_{\sigma }(i{\omega }_{n})\), or \({\Delta }_{\sigma }(i{\omega }_{n})\) can be viewed as a “dynamical mean field” acting on particles on a site, since they all appear in the bilinear term of the local action (7.32).
- 8.
In the following we only consider the paramagnetic phase, whereas magnetic order is assumed to be suppressed (“frustrated”).
- 9.
Here we assume for simplicity that the metal remains a Fermi liquid and the insulator stays paramagnetic down to the lowest temperatures.
- 10.
We note that \(\hat{{H}}_{\mathrm{LDA}}^{0}\) may include additional non-interacting orbitals.
References
J.H. de Boer, E.J.W. Verwey, Proc. Phys. Soc. 49, 59 (1937)
N.F. Mott, R. Peierls, Proc. Phys. Soc. A 49, 72 (1937)
M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)
M.C. Gutzwiller, Phys. Rev. Lett. 10, 59 (1963)
J. Hubbard, Proc. Roy. Soc. Lond. A276, 238 (1963)
J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)
E. Lieb, F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)
D. Vollhardt, in Lectures on the Physics of Strongly Correlated Systems XIV, ed. by A. Avella, F. Mancini. AIP Conference Proceedings, vol. 1297 (American Institute of Physics, Melville, 2010), p. 339
D. Vollhardt, in Correlated Electron Systems, ed. by V.J. Emery (World Scientific, Singapore, 1993), p. 57
R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1982)
C. Itzykson, J.M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989)
W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
U. Wolff, Nucl. Phys. B 225, 391 (1983)
E. Müller-Hartmann, Z. Phys. B 74, 507 (1989)
W. Metzner, Z. Phys. B 77, 253 (1989)
E. Müller-Hartmann, Z. Phys. B 76, 211 (1989)
H. Schweitzer, G. Czycholl, Solid State Comm. 69, 171 (1989)
H. Schweitzer, G. Czycholl, Z. Phys. B 83, 93 (1991)
U. Brandt, C. Mielsch, Z. Phys. B 75, 365 (1989)
P.G.J. van Dongen, F. Gebhard, D. Vollhardt, Z. Phys. 76, 199 (1989)
F. Kajzar, J. Friedel, J. Phys. (Paris) 39, 397 (1978)
G. Treglia, F. Ducastelle, D. Spanjaard, Phys. Rev. B 22, 6472 (1980)
G. Bulk, R.J. Jelitto, Phys. Rev. B 41, 413 (1990)
J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960)
V. Janiš, Z. Phys. B 83, 227 (1991)
V. Janiš, D. Vollhardt, Int. J. Mod. Phys. B 6, 731 (1992)
B. Velický, S. Kirkpatrick, H. Ehrenreich, Phys. Rev. 175, 745 (1968)
F. Yonezawa, K. Morigaki, Suppl. Prog. Theor. Phys. 53, 1 (1973)
R.J. Elliot, J.A. Krumhansl, P.L. Leath, Rev. Mod. Phys. 46, 465 (1974)
R. Vlaming, D. Vollhardt, Phys. Rev. B 45, 4637 (1992)
A. Georges, G. Kotliar, Phys. Rev. B 45, 6479 (1992)
M. Jarrell, Phys. Rev. Lett. 69, 168 (1992)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
M. Fabrizio, in Lectures on the Physics of Highly Correlated Electron Systems XI, ed. by A. Avella, F. Mancini. AIP Conference Proceedings, vol. 918 (American Institute of Physics, Melville, 2007), p. 3
J.E. Hirsch, R.M. Fye, Phys. Rev. Lett. 56, 2521 (1986)
J.K. Freericks, V. Zlatić, Rev. Mod. Phys. 75, 1333 (2003)
R. Bulla, Phys. Rev. Lett. 83, 136 (1999)
R. Bulla, T.A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)
M. Karski, C. Raas, G.S. Uhrig, Phys. Rev. B 77, 075116 (2008)
M. Caffarel, W. Krauth, Phys. Rev. Lett. 72, 1545 (1994)
Q. Si, M.J. Rozenberg, G. Kotliar, A.E. Ruckenstein, Phys. Rev. Lett. 72, 2761 (1994)
M.J. Rozenberg, G. Moeller, G. Kotliar, Mod. Phys. Lett. B 8, 535 (1994)
M.J. Rozenberg, X.Y. Zhang, G. Kotliar, Phys. Rev. Lett. 69, 1236 (1992)
A. Georges, W. Krauth, Phys. Rev. Lett. 69, 1240 (1992)
A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, Phys. Rev. B 72, 035122 (2005)
P. Werner, A. Comanac, L. de’ Medici, M. Troyer, A.J. Millis, Phys. Rev. Lett. 97, 076405 (2006)
K. Haule, Phys. Rev. B 75, 155113 (2007)
X.Y. Zhang, M.J. Rozenberg, G. Kotliar, Phys. Rev. Lett. 70, 1666 (1993)
K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A.K. McMahan, R.T. Scalettar, T. Pruschke, V.I. Anisimov, D. Vollhardt, Psi-k Newsletter 56, 65 (2003); Reprinted in Phys. Status Solidi B 243, 2599 (2006)
N.E. Bickers, D.J. Scalapino, Ann. Phys. (NY) 193, 206 (1989)
A.I. Lichtenstein, M.I. Katsnelson, J. Phys. Condens. Matter 11, 1037 (1999)
G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)
V. Drchal, V. Janiš, J. Kudrnovský, V.S. Oudovenko, X. Dai, K. Haule, G. Kotliar, J. Phys. Condens. Matter 17, 61 (2005)
D.E. Logan, M.T. Glossop, J. Phys. Condens. Matter 12, 985 (2000)
A. Kauch, K. Byczuk, ArXiv:0912.4278 (2009)
V. Janiš, P. Augustinský, Phys. Rev. B 75, 165108 (2007)
T. Pruschke, M. Jarrell, J.K. Freericks, Adv. Phys. 44, 187 (1995)
A. Georges, in Lectures on the Physics of Highly Correlated Electron Systems VIII, ed. by A. Avella, F. Mancini. AIP Conference Proceedings, vol. 715 (American Institute of Physics, Melville, 2004), p. 3
G. Kotliar, D. Vollhardt, Phys. Today 57(3), 53 (2004)
N.F. Mott, Rev. Mod. Phys. 40, 677 (1968)
N.F. Mott, Metal-Insulator Transitions, 2nd edn. (Taylor and Francis, London, 1990)
F. Gebhard, The Mott Metal-Insulator Transition (Springer, Berlin, 1997)
D.B. McWhan, J.P. Remeika, Phys. Rev. B 2, 3734 (1970)
D.B. McWhan, A. Menth, J.P. Remeika, W.F. Brinkman, T.M. Rice, Phys. Rev. B 7, 1920 (1973)
T.M. Rice, D.B. McWhan, IBM J. Res. Develop. 14, 251 (1970)
J. Hubbard, Proc. Roy. Soc. Lond. A281, 401 (1964)
W.F. Brinkman, T.M. Rice, Phys. Rev. B 2, 4302 (1970)
K. Byczuk, M. Kollar, K. Held, Y.F. Yang, I.A. Nekrasov, T. Pruschke, D. Vollhardt, Nat. Phys. 3, 168 (2007)
A. Toschi, M. Capone, C. Castellani, K. Held, Phys. Rev. Lett. 102, 076402 (2009)
C. Raas, P. Grete, G.S. Uhrig, Phys. Rev. Lett. 102, 076406 (2009)
A. Lanzara, P.V. Bogdanov, X.J. Zhou, S.A. Kellar, D.L. Feng, E.D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, Z.X. Shen, Nature 412, 510 (2001)
Z.X. Shen, A. Lanzara, S. Ishihara, N. Nagaosa, Philos. Mag. B 82, 1349 (2002)
H. He, Y. Sidis, P. Bourges, G.D. Gu, A. Ivanov, N. Koshizuka, B. Liang, C.T. Lin, L.P. Regnault, E. Schoenherr, B. Keimer, Phys. Rev. Lett. 86, 1610 (2001)
J. Hwang, T. Timusk, G.D. Gu, Nature 427, 714 (2004)
A. Hofmann, X.Y. Cui, J. Schäfer, S. Meyer, P. Höpfner, C. Blumenstein, M. Paul, L. Patthey, E. Rotenberg, J. Bünemann, F. Gebhard, T. Ohm, W. Weber, R. Claessen, Phys. Rev. Lett. 102, 187204 (2009)
R. Bulla, T.A. Costi, D. Vollhardt, Phys. Rev. B 64, 045103 (2001)
S.K. Mo, H.D. Kim, J.W. Allen, G.H. Gweon, J.D. Denlinger, J.H. Park, A. Sekiyama, A. Yamasaki, S. Suga, P. Metcalf, K. Held, Phys. Rev. Lett. 93, 076404 (2004)
M.J. Rozenberg, R. Chitra, G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999)
J. Joo, V. Oudovenko, Phys. Rev. B 64, 193102 (2001)
N. Blümer, Metal-Insulator Transition and Optical Conductivity in High Dimensions (Shaker, Aachen, 2003)
T. Pruschke, Prog. Theor. Phys. Suppl. 160, 274 (2005)
D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990)
H. Park, K. Haule, G. Kotliar, Phys. Rev. Lett. 101, 186403 (2008)
P. Hohenberg, W. Kohn, Phys. Rev. 136B, 864 (1964)
W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)
R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)
V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)
V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, J. Phys. Cond. Matter 9, 767 (1997)
V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, G. Kotliar, J. Phys.: Cond. Matt. 9, 7359 (1997)
A.I. Lichtenstein, M.I. Katsnelson, Phys. Rev. B 57, 6884 (1998)
I.A. Nekrasov, K. Held, N. Blümer, A.I. Poteryaev, V.I. Anisimov, D. Vollhardt, Eur. Phys. J. B 18, 55 (2000)
K. Held, I.A. Nekrasov, N. Blümer, V.I. Anisimov, D. Vollhardt, Int. J. Mod. Phys. B 15, 2611 (2001)
K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A.K. McMahan, R. Scalettar, T. Pruschke, V. Anisimov, D. Vollhardt, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, ed. by J. Grotendorst, D. Marks, A. Muramatsu. NIC Series Volume, vol. 10, (NIC Directors, Forschungszentrum Jülich, Berlin, 2002), p. 175
A.I. Lichtenstein, M.I. Katsnelson, G. Kotliar, in Electron Correlations and Materials Properties, ed. by A. Gonis, N. Kioussis, M. Ciftan (Kluwer, New York, 2002), p. 428
K. Held, Adv. Phys. 56, 829 (2007)
M.I. Katsnelson, V.Y. Irkhin, L. Chioncel, A.I. Lichtenstein, R.A. de Groot, Rev. Mod. Phys. 80, 315 (2008)
V. Anisimov, Y. Izyumov, Electronic Structure of Correlated Materials, Springer Series in Solid-State Sciences, vol. 163 (Springer, Berlin, 2010)
J. Kuneš, I. Leonov, M. Kollar, K. Byczuk, V.I. Anisimov, D. Vollhardt, Eur. Phys. J. Special Topics 180, 5 (2010)
M. Jarrell, J.E. Gubernatis, Phys. Rep. 269, 133 (1996)
M. Potthoff, Adv. Solid State Phys. 45, 135 (2005)
T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)
K. Held, A.A. Katanin, A. Toschi, Prog. Theor. Phys. Suppl. 176, 117 (2008)
A. Fujimori, I. Hase, H. Namatame, Y. Fujishima, Y. Tokura, H. Eisaki, S. Uchida, K. Takegahara, F.M.F. de Groot, Phys. Rev. Lett. 69, 1796 (1992)
A. Sekiyama, H. Fujiwara, S. Imada, S. Suga, H. Eisaki, S.I. Uchida, K. Takegahara, H. Harima, Y. Saitoh, I.A. Nekrasov, G. Keller, D.E. Kondakov, A.V. Kozhevnikov, T. Pruschke, K. Held, D. Vollhardt, V.I. Anisimov, Phys. Rev. Lett. 93, 156402 (2004)
I.A. Nekrasov, G. Keller, D.E. Kondakov, A.V. Kozhevnikov, T. Pruschke, K. Held, D. Vollhardt, V.I. Anisimov, Phys. Rev. B 72, 155106 (2005)
E. Pavarini, S. Biermann, A. Poteryaev, A.I. Lichtenstein, A. Georges, O.K. Andersen, Phys. Rev. Lett. 92, 176403 (2004)
I.H. Inoue, I. Hase, Y. Aiura, A. Fujimori, K. Morikawa, T. Mizokawa, Y. Haruyama, T. Maruyama, Y. Nishihara, Physica C 235–240, 1007 (1994)
P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)
N.F. Mott, Proc. Phys. Soc. Lond., Sect. A 62, 415 (1949)
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
V. Janiš, D. Vollhardt, Phys. Rev. B 46, 15712 (1992)
V. Janiš, M. Ulmke, D. Vollhardt, Europhys. Lett. 24, 287 (1993)
M. Ulmke, V. Janiš, D. Vollhardt, Phys. Rev. B 51, 10411 (1995)
V. Dobrosavljević, G. Kotliar, Phys. Rev. B 50, 1430 (1994)
M.C.O. Aguiar, V. Dobrosavljević, E. Abrahams, G. Kotliar, Phys. Rev. B 73, 115117 (2006)
M. Potthoff, M. Balzer, Phys. Rev. B 75, 125112 (2007)
V. Janiš, D. Vollhardt, Phys. Rev. B 46, 15712 (1992)
V. Dobrosavljević, G. Kotliar, Phys. Rev. Lett. 78, 3943 (1997)
V. Dobrosavljević, A.A. Pastor, B.K. Nikolić, Europhys. Lett. 62, 76 (2003)
F.X. Bronold, A. Alvermann, H. Fehske, Phil. Mag. 84, 637 (2004)
K. Byczuk, W. Hofstetter, D. Vollhardt, Phys. Rev. Lett. 94, 056404 (2005)
K. Byczuk, W. Hofstetter, D. Vollhardt, Phys. Rev. Lett. 102, 146403 (2009)
K. Byczuk, M. Ulmke, D. Vollhardt, Phys. Rev. Lett. 90, 196403 (2003)
K. Byczuk, M. Ulmke, Eur. Phys. J. B 45, 449 (2005)
K. Byczuk, W. Hofstetter, D. Vollhardt, Phys. Rev. B 69, 045112 (2004)
P. Lombardo, R. Hayn, G.I. Japaridze, Phys. Rev. B 74, 085116 (2006)
M. Potthoff, M. Balzer, Phys. Rev. B 75, 125112 (2007)
U. Yu, K. Byczuk, D. Vollhardt, Phys. Rev. Lett. 100, 246401 (2008)
R.J. Anglin, W. Ketterle, Nature 416, 211 (2002)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, U. Sen, Adv. Phys. 56, 243 (2007)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)
A. Isacsson, M.C. Cha, K. Sengupta, S.M. Girvin, Phys. Rev. B 72, 184507 (2005)
S.D. Huber, E. Altman, H.P. Büchler, G. Blatter, Phys. Rev. B 75, 085106 (2007)
A. Micheli, G.K. Brennen, P. Zoller, Nature 2, 341 (2006)
M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)
K. Byczuk, D. Vollhardt, Phys. Rev. B 77, 235106 (2008)
A. Hubener, M. Snoek, W. Hofstetter, Phys. Rev. B 80, 245109 (2009)
W.J. Hu, N.H. Tong, Phys. Rev. B 80, 245110 (2009)
P. Anders, E. Gull, L. Pollet, M. Troyer, P. Werner, Phys. Rev. Lett. 105, 096402 (2010)
K. Byczuk, D. Vollhardt, Ann. Phys. (Berlin) 18, 622 (2009)
J. Dziarmaga, Adv. Phys. 59, 1063 (2010)
A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)
L. Perfetti, P.A. Loukakos, M. Lisowski, U. Bovensiepen, H. Berger, S. Biermann, P.S. Cornaglia, A. Georges, M. Wolf, Phys. Rev. Lett. 97, 067402 (2006)
S. Wall, D. Brida, S.R. Clark, H.P. Ehrke, D. Jaksch, A. Ardavan, S. Bonora, H. Uemura, Y. Takahashi, T. Hasegawa, H. Okamoto, G. Cerullo, A. Cavalleri, Nat. Phys. 7, 114 (2011)
P. Schmidt, H. Monien, arXiv:cond-mat/0202046
V. Turkowski, J.K. Freericks, Phys. Rev. B 71, 085104 (2005)
R. van Leeuwen, N.E. Dahlen, G. Stefanucci, C.O. Almbladh, U. von Barth, in Time-Dependent Density Functional Theory, ed. by M.A.L. Marques, C.A. Ullrich, F. Nogueira, A. Rubio, K. Burke, E.K.U. Gross. Lecture Notes in Physics, vol. 706 (Springer, Berlin, 2006)
M. Eckstein, M. Kollar, P. Werner, Phys. Rev. B 81, 115131 (2010)
M. Eckstein, M. Kollar, P. Werner, Phys. Rev. Lett. 103, 056403 (2009)
M. Eckstein, P. Werner, Phys. Rev. B 82, 115115 (2010)
M. Eckstein, A. Hackl, S. Kehrein, M. Kollar, M. Moeckel, P. Werner, F.A. Wolf, Eur. Phys. J. Special Topics 180, 217 (2010)
J.K. Freericks, H.R. Krishnamurthy, T. Pruschke, Phys. Rev. Lett. 102, 136401 (2009)
M. Eckstein, M. Kollar, Phys. Rev. B 78, 245113 (2008)
B. Moritz, T.P. Devereaux, J.K. Freericks, Phys. Rev. B 81, 165112 (2010)
M. Eckstein, M. Kollar, Phys. Rev. B 78, 205119 (2008)
J.K. Freericks, V.M. Turkowski, V. Zlatić, Phys. Rev. Lett. 97, 266408 (2006)
M.T. Tran, Phys. Rev. B 78, 125103 (2008)
J.K. Freericks, Phys. Rev. B 77, 075109 (2008)
A.V. Joura, J.K. Freericks, T. Pruschke, Phys. Rev. Lett. 101, 196401 (2008)
N. Tsuji, T. Oka, H. Aoki, Phys. Rev. B 78, 235124 (2008)
N. Tsuji, T. Oka, H. Aoki, Phys. Rev. Lett. 103, 047403 (2009)
M. Eckstein, T. Oka, P. Werner, Phys. Rev. Lett. 105, 146404 (2010)
N. Tsuji, T. Oka, P. Werner, H. Aoki, Phys. Rev. Lett. 106, 236401 (2011)
M. Eckstein, M. Kollar, Phys. Rev. Lett. 100, 120404 (2008)
M. Eckstein, M. Kollar, New J. Phys. 12, 055012 (2010)
N. Eurich, M. Eckstein, P. Werner, Phys. Rev. B 83, 155122 (2011)
M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)
M. Moeckel, S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)
M. Moeckel, S. Kehrein, Ann. Phys. 324, 2146 (2009)
M. Greiner, O. Mandel, T.W. Hänsch, I. Bloch, Nature 419, 51 (2002)
A. Rapp, G. Zarand, C. Honerkamp, W. Hofstetter, Phys. Rev. Lett. 98, 160405 (2007)
M. Snoek, I. Titvinidze, C. Toke, K. Byczuk, W. Hofstetter, New J. Phys. 10, 093008 (2008)
U. Schneider, L. Hackermüller, S. Will, T. Best, I. Bloch, T.A. Costi, R.W. Helmes, D. Rasch, A. Rosch, Science 322, 1520 (2008)
J.K. Freericks, Transport in Multilayered Nanostructures – The Dynamical Mean-Field Approach (Imperial College Press, London, 2006)
M. Potthoff, W. Nolting, Phys. Rev. B 59, 2549 (1999)
M. Takizawa, H. Wadati, K. Tanaka, M. Hashimoto, T. Yoshida, A. Fujimori, A. Chikamtsu, H. Kumigashira, M. Oshima, K. Shibuya, T. Mihara, T. Ohnishi, M. Lippmaa, M. Kawasaki, H. Koinuma, S. Okamoto, A.J. Millis, Phys. Rev. Lett. 97, 057601 (2006)
L. Chen, J.K. Freericks, Phys. Rev. B 75, 1251141 (2007)
K. Byczuk, in Condensed Matter Physics in the Prime of the 21st Century: Phenomena, Materials, Ideas, Methods, ed. by J. Jedrzejewski (World Scientific, Singapore, 2008), p. 1
R.W. Helmes, T.A. Costi, A. Rosch, Phys. Rev. Lett. 100, 056403 (2008)
Acknowledgments
We thank Jim Allen, Vladimir Anisimov, Nils Blümer, Ralf Bulla, Liviu Chioncel, Theo Costi, Vlad Dobrosavljević, Peter van Dongen, Martin Eckstein, Volker Eyert, Florian Gebhard, Karsten Held, Walter Hofstetter, Vaclav Janiš, Anna Kauch, Stefan Kehrein, Georg Keller, Gabi Kotliar, Jan Kuneš, Ivan Leonov, Walter Metzner, Michael Moeckel, Igor Nekrasov, Thomas Pruschke, Xinguo Ren, Shigemasa Suga, Götz Uhrig, Martin Ulmke, Ruud Vlaming, Philipp Werner, and Unjong Yu for valuable collaborations. Support by the Deutsche Forschungsgemeinschaft through TRR 80 and FOR 1346 is gratefully acknowledged. KB was also supported by the grant N N202 103138 of the Polish Ministry of Science and Education.
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Vollhardt, D., Byczuk, K., Kollar, M. (2012). Dynamical Mean-Field Theory. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21831-6_7
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