Organisers

• Patrick Rinke (Fritz-Haber Institute of the Max-Planck Society, Berlin, Germany)
• Matthias Scheffler (Fritz-Haber-Institute, Berlin, Germany)

Supports

   Psi-k

European Theoretical Spectroscopy Facility (ETSF)

   CECAM

Description

The term "strongly correlated" typically refers to systems or phenomena in which the single-particle picture and first-order perturbation theory for the self energy fail to describe the electronic properties. However, several other - often conflicting - definitions are in circulation. A large class of materials often classified as strongly correlated contain localized d- or f-electrons. The simultaneous presence of strongly localized electrons and itinerant band states, structural, orbital and spin degrees of freedom and strong Coulomb interactions gives rise to a rich variety of physics and chemistry that makes these materials attractive for a wide range of applications. 

One of the hallmarks of strongly correlated systems, that is often used to classify a system as such, is the failure of density functional theory (DFT) in the local-density or generalized gradient approximation (LDA or GGA, respectively). The major deficiencies of LDA and GGA in this context is the delocalization (or self-interaction) error [1], which is particularly severe for systems with partially occupied d- or f-states and can even lead to qualitatively incorrect metallic ground states for many insulating systems. Hybrid functionals, on the other hand, partly correct the self-interaction error by incorporating a certain portion of exact exchange, which significantly improves the descriptions of d- or f-electron systems [2,3]. The dependence on adjustable parameters, however, remains a concern. 

Conversely, correlation effects that govern the physics of localized f-electrons can in principle be treated systematically by dynamical mean field theory (DMFT) [4,5]. The Kondo resonance in Cerium [6] and the Mott-transition [7,8] are only two examples of successful DMFT applications. However, in practice the many-body corrections in DMFT are only applied locally to an atomic site (e.g., the Anderson impurity model) and the impurity solvers require input parameters (such as the Hubbard U) for the interaction strength. Moreover, most existing DMFT schemes are coupled (non-self-consistently) to local or semilocal DFT calculations and the description of the itinerant electrons therefore remains on the level of LDA and GGA.

Many-body perturbation theory (MBPT) provides an alternative approach to the problem [9]. Hedin's GW approximation to the many-body self energy [10] would be a first logical step towards a systematic ab initio understanding of strongly correlated systems. The GW approach corresponds to the first order term of a systematic expansion in MBPT [10] and has become the method of choice for the description of quasiparticle band structures in weakly correlated solids [11]. Through the screened Coulomb interaction W it captures the screening among itinerant electrons while at the same time treating exchange at the exact exchange level. The latter should account for a large part of the interactions among localized d- or f-electrons, with the additional advantage that localized and itinerant states are treated on the same footing. The first promising calculations to strongly correlated materials [12,13] and correlated phenomena like the Kondo resonance in quantum transport [14,15] are emerging, but it is not clear at present when the GW approximation would break down and how to go beyond it. Combining DMFT and GW might give the best of both worlds [9,16], but so far no implementation or application has been demonstrated.

Increasing the level of abstraction leads away from real materials to quantum lattice models. The Hubbard or the Anderson model are promiment examples and are studied intensively to gain a deeper understanding of strongly correlated phenomena. The literature on strongly correlated model systems is too vast to summarize recent progress comprehensively. However, a few examples include kinks in the dispersion of energy bands caused by many-body correlation effects [17], disorder induced ferromagnetism and the emergence of an alloy Kondo insulator [18] and a new efficient perturbation theory that incorporates also long-range correlations [19].

References

[1] A. J. Cohen, Paula Mori-Sánchez and Weitao Yang, Science 321, 792 (2008).
[2] J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer,
and G. Kresse Phys. Rev. B 75, 045121 (2007).
[3] K. N. Kudin, G. E. Scuseria, and R. L. Martin, Phys. Rev. Lett. 89, 266402 (2002).
[4] K. Held, Advances in Physics 56, 829 (2007).
[5] G. Kotliar et al., Rev. Mod. Phys. 78, 865 (2006).
[6] B. Amadon, S. Biermann, A. Georges, and F. Aryasetiawan, Phys. Rev. Lett. 96, 066402 (2006).
[7] O. Parcollet, G. Biroli, and G. Kotliar, Phys. Rev. Lett. 92, 226402 (2004).
[8] T. Ohashi, T. Momoi, H. Tsunetsugu, and N. Kawakami, Phys. Rev. Lett. 100, 076402 (2008).
[9] F. Aryasetiawan, J. M. Tomczak, T. Miyake, and R. Sakuma, Phys. Rev. Lett. 102, 176402 (2009).
[10] L. Hedin, Phys. Rev. 139, A796 (1965).
[11] P. Rinke, A. Qteish, J. Neugebauer, C. Freysoldt, and M. Scheffler, New J. Phys. 7, 126 (2005).
[12] H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 (2009).
[13] M. Gatti, F. Bruneval, V. Olevano, and L. Reining, Phys. Rev. Lett. 99, 266402 (2007).
[14] K. S. Thygesen and A. Rubio, J. Chem. Phys. 126, 091101 (2007).
[15] C. D. Spataru, M. S. Hybertsen, S. G. Louie, and A. J. Millis, Phys. Rev. B 79, 155110 (2009).
[16] S. Biermann, F. Aryasetiawan, and A. Georges, Phys. Rev. Lett. 90, 086402 (2003).
[17] K. Byczuk, M. Kollar, K. Held, Y.-F. Yang, I. A. Nekrasov, Th. Pruschke,
and D. Vollhardt, Nature Physics 3, 168 (2007)
[18] U. Yu, K. Byczuk, and D. Vollhardt, Phys. Rev. Lett. 100, 246401 (2008).
[19] H. Hafermann, G. Li, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein,
and H. Monien, Phys. Rev. Lett. 102, 206401 (2009)