XIV Training Course in the Physics of Strongly Correlated Systems


Vietri sul Mare (Salerno) Italy

5 - 16 October 2009


Lecture Topics and Background References


Professor Vladimir I. Anisimov

Institute of Metal Physics Russian Academy of Sciences - Ural Division Yekaterinburg Russia

Electronic structure calculations for systems with strong Coulomb correlations




. Correlation effect and electronic structure calculations
a) Model Hamiltonians and ab-initio approaches
b) Density Functional Theory and its applications
2. Combining model approaches and Density Functional Theory
a) Wannier functions and model Hamiltonian construction
b) Static mean-field approach: LDA+U method
3. LDA+U method applications to real materials
a) Mott-insulators
b) Orbital, charge and spin ordering
4. LDA+DMFT method
a) LDA+DMFT calculation scheme
b) Impurity solvers
5. LDA+DMFT method applications to real materials
a) Strongly correlated metals
b) Metal-insulator transitions





Professor Anders W. Sandvik

Department of Physics, Boston University, Boston MA,USA

Computational studies of quantum spin systems





These lectures will give an introduction to some of the computational techniques used to study quantum spin systems, primarly spin-1/2 models such as the Heisenberg model and extensions of it. Practical use of the methods will be illustrated by examples. In these applications, the main goal is to characterize different types of ordered and disordered ground states and quantum phase transitions between them.


. Exact diagonalization studies
a) Use of symmetries for block-diagonalization
b) Studies of ground states and excitations with the Lanczos method
2. Stochastic series expansion (quantum Monte Carlo)
a) Algorithm for the spin-1/2 Heisenberg model
b) Studies of systems in one and two dimensions
3. Methods formulated in the valence-bond basis
a) The valence-bond basis and amplitude-product states
b) Variational and projector quantum Monte Carlo methods
4. Studies of quantum phase transitions
a) Finite-size scaling techniques
b) Neel to Valence-bond-solid transition
5. Disordered (random) systems
a) The diluted two-dimensional Heisenberg model
b) Low-energy dynamics; sum rules and triplet localization


For the afternoon training sessions, the instructor will make available simple computer programs using the algorithms discussed in the lectures.
These programs are written in Fortran 90. A good reference for this programming language is; Fortran 90/95 for Scientists and Engineers, by S. Chapman (McGraw Hill, 2004). Participants with their own laptops are urged to install a Fortran 90/95 compiler, e.g., "g95", available for free at www.g95.org.




  Professor George Sawatzky

Department of Physics and Astronomy, University of British Columbia, Vancouver B.C., Canada

Electronic structure of strongly correlated complex oxide systems




1. Basics of the electronic structure of strongly correlated electron system: why not DFT
2. Why are 3d transition metal and rare earths special and experimental tools to demonstrate this
3. Description of some models and of correlated systems and some exotic effects expected
4. Parameter determination and the standard theories of screening and the effects in real materials with nonuniform polarizabilities leading to unconventional "screening"
5. Interplay between orbital-spin, charge and lattice degrees of freedom – highTc's Fe pnictides, surfaces and interfaces.




  Professor Dieter Vollhardt

Center for Electronic Correlations and Magnetism, University of Augsburg, Augsburg, Germany

Theory of correlated fermionic condensed matter





1. Correlated electrons made simple.
a) What are electronic correlations and where do they show up?
b) Introduction to dynamical mean-field theory (DMFT) [1,2].
2. Electronic correlations - from models to materials.
a) DMFT and the Mott-Hubbard metal-insulator transition [1,2].
b) Merging DMFT with density functional theory (LDA+DMFT) [1,3].
3. Correlation-induced phenomena in electronic systems.
a) Correlation effects in transition metal oxides [3].
b) Kinks in the electronic dispersion [4].

4. Correlated electrons in the presence of disorder.
a) Non-interacting electrons with disorder: Anderson localization [5].
b) Mott-Hubbard transition versus Anderson localization [6].
5. Helium-3, Prototype of a correlated Fermi system [7].
a) Superfluid He-3: From very low temperatures to the big bang [8].
b) Common concepts in correlated Fermi systems.

Public lecture (Friday afternoon):
"Magnetism: A Guided Tour from Ancient Greece to Modern Salerno"



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