Abstract
We present an efficient impurity solver for the dynamical mean-field theory (DMFT). It is based on the separation of bath degrees of freedom into the low energy and the high energy parts. The former is solved exactly using exact diagonalization and the latter is treated approximately using Green’s function equation of motion decoupling approximation. The two parts are combined coherently under the standard basis operator formalism. The impurity solver is applied to the Anderson impurity model and, combined with DMFT, to the one-band Hubbard model. Qualitative agreement is found with other well established methods. Some promising features and possible improvements of the present solver are discussed.
Similar content being viewed by others
References
W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
A. Georges, G. Kotliar, W. Krauth, M. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
K. Held, Adv. Phys. 56, 829 (2007)
A. Liebsch, Phys. Rev. B 70, 165103 (2004)
P. Werner, A.J. Millis, Phys. Rev. Lett. 99, 126405 (2007)
A. Georges, L. de Medici, J. Mravlje, Annu. Rev. Condens. Matter Phys. 4, 137 (2013)
G. Kotliar, S.Y. Savrasov, G. Pálsson, G. Biroli, Phys. Rev. Lett. 87, 186401 (2001)
M.H. Hettler et al., Phys. Rev. B. 58, R7475 (1998)
T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)
J.E. Hirsch, R.M. Fye, Phys. Rev. Lett. 56, 2521 (1986)
N. Blümer, Phys. Rev. B 76, 205120 (2007)
P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)
P. Werner, A.J. Millis, Phys. Rev. B 74, 155107 (2006)
A.N. Rubtsov, A.I. Lichtenstein, J. Exp. Theor. Phys. Lett. 80, 61 (2004)
E. Gull et al., Rev. Mod. Phys. 83, 349 (2011)
M. Jarrell, J. Gubernatis, Phys. Rep. 269, 133 (1996)
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
R. Bulla, Theo A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)
M. Caffarel, W. Krauth, Phys. Rev. Lett. 72, 1545 (1994)
Q. Si, M.J. Rozenberg, K. Kotliar, A.E. Ruckenstein, Phys. Rev. Lett. 72, 2761 (1994)
M.J. Rozenberg, G. Moeller, G. Kotliar, Mod. Phys. Lett. B 8, 535 (1994)
A. Liebsch, Phys. Rev. B 84, 180505(R) (2011)
A. Georges, G. Kotliar, Phys. Rev. B 45, 6479 (1992)
X. Dai, K. Haule, G. Kotliar, Phys. Rev. B 72, 045111 (2005)
J.N. Zhuang, Q.M. Liu, Z. Fang, X. Dai, Chin. Phys. B 19, 087104 (2010)
K. Aryanpour, M.H. Hettler, M. Jarrell, Phys. Rev. B 67, 085101 (2003)
N.E. Bickers, Rev. Mod. Phys. 59, 845 (1987)
T. Pruschke, D.L. Cox, M. Jarrell, Phys. Rev. B 47, 3553 (1993)
K. Haule, S. Kirchner, J. Kroha, P. Wölflle, Phys. Rev. B 64, 155111 (2001)
J.N. Zhuang, L. Wang, Z. Fang, X. Dai, Phys. Rev. B 79 165114 (2009)
C. Gros, Phys. Rev. B 50, 7295 (1994)
H.O. Jeschke, G. Kotliar, Phys. Rev. B 71, 085103 (2005)
J.X. Zhu, R.C. Albers, G. Kotliar, Mod. Phys. Lett. B 20, 1629 (2006)
Q. Feng, Y.Z. Zhang, H.O. Jeschke, Phys. Rev. B79, 235112 (2009)
Q. Feng, P.M. Oppeneer, J. Phys.: Condens. Matter 24, 055603 (2012)
H. Hafermann et al., Europhys. Lett. 85, 27007 (2009)
J.P. Julien, R.C. Albers, arXiv:0810.3302 (2008)
M. Granath, H.U.R. Strand, Phys. Rev. B 86, 115111 (2012)
R.Q. He, Z.Y. Lu, Phys. Rev. B 89, 085108 (2014)
Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Phys. Rev. B 90, 085102 (2014)
Z.H. Li et al., Phys. Rev. Lett. 109, 266403 (2012)
D. Hou et al., Phys. Rev. B 90, 045141 (2014)
J. Hubbard, Proc. R. Soc. London 281, 401 (1964)
F. Gebhard, The Mott Metal-Insulator Transition (Springer-Verlag, Berlin, Heidelberg, 1997)
S.B. Haley, P. Erdös, Phys. Rev. B 5, 1106 (1972)
S.B. Haley, Phys. Rev. B 17, 337 (1978)
C. Lacroix, J. Phys. C 11, 2389 (1981)
C. Lacroix, J. Appl. Phys. 53, 2131 (1982)
H.G. Luo, J.J. Ying, S.J. Wang, Phys. Rev. B 59, 9710 (1999)
R. Bulla, M. Potthoff, Eur. Phys. J. B 13, 257 (2000)
M. Potthoff, Phys. Rev. B 64, 165114 (2001)
R. Bulla, Phys. Rev. Lett. 83, 136 (1999)
N.H. Tong, S.Q. Shen, F.C. Pu, Phys. Rev. B 64, 235109 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H., Tong, NH. A standard basis operator equation of motion impurity solver for dynamical mean field theory. Eur. Phys. J. B 88, 319 (2015). https://doi.org/10.1140/epjb/e2015-60082-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2015-60082-9