Andersen Group El.-Phon. QMC C60 Resistivity saturation

Cluster Dynamical Mean-Field methods

Cluster dynamical mean-field methods provide useful tools for treating systems with strong correlation. In contrast to traditional Quantum Monte-Carlo (QMC) methods, these methods treat infinite systems, which is particularly useful when studying phase transitions. In these methods a cluster is embedded in self-consistently determined host, describing the rest of an infinite system. Spatial correlation is treated accurately over a distance comparable to the cluster size and in a mean-field spirit for larger distances.

There are mainly two type of methods, the dynamical cluster approximation (DCA) and the cluster dynamical mean-field theory (CDMFT). DCA is formulated in reciprocal space and it keeps the periodicity of the system, i.e., the momentum is a good quantum number. CDMFT is formulated in real space.

These approaches require methods for solving cluster problems. We have written computer programs using two methods, Exact Diagonalization (ED) and the Hirsch-Fye (HF) QMC method, adapted to the CDMFT and DCA approaches.

These methods have been used to study the one-dimensional Hubbard model and the pseudogap in High Tc cuprates with or without phonons.

E. Koch, G. Sangiovanni, and O. Gunnarsson:
Sum rules and bath parametrization for quantum cluster theories
Phys. Rev. B 78, 115102 (2008).

O. Gunnarsson, M.W. Haverkort, G. Sangiovanni:
Fourier transformation and response functions,
Phys. Rev. B 82, 233104 (2010).

A. Valli, G. Sangiovanni, O. Gunnarsson, A. Toschi, K. Held:
Dynamical vertex approximation for nanoscopic systems,
Phys. Rev. Lett. 104, 246402 (2010).

G. Sangiovanni and O. Gunnarsson:
Isotope effect in the pseudogap state of high-temperature copper-oxide superconductors,
Phys. Rev. B, Rapid Commun. 84, 100505 (2011).

J. Merino and O. Gunnarsson:
Pseudogap in cuprate and organic superconductors,
For further information contact Olle Gunnarsson (, Giorgio Sangiovanni ( or Erik Koch (

Max-Planck Institut für Festkörperforschung
Postfach 800 665 D-70506 Stuttgart

Last Update: September 2012
Andersen Group