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
Lectures:
1. 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
References:
Department of Physics, Boston University, Boston MA,USA
Computational studies of quantum spin systems
Summary:
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.
Lectures:
1. 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
Tutorials:
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.
References:
1. E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).
2. A. W. Sandvik, Phys. Rev. B 59, R14157 (1999); O. F. Syljuasen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002).
3. A. W. Sandvik, Phys. Rev. Lett. 95, 207203 (2005); J. Lou and A. W. Sandvik, Phys. Rev. B 76, 104432 (2007).
4. S. Sachdev, Nature Physics 4, 173 (2008); A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007); J. Lou, A. W. Sandvik, and N. Kawashima, arXiv:0908.0740.
5. A. W. Sandvik, Phys. Rev. B 66, 024418 (2002); L. Wang and A. W. Sandvik,
Phys. Rev. Lett. 97, 117204 (2006).
Department of Physics and Astronomy, University of British Columbia, Vancouver B.C., Canada
Electronic structure of strongly correlated complex oxide systems
Lectures:
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.
Center for Electronic Correlations and Magnetism, University of Augsburg, Augsburg, Germany
Theory of correlated fermionic condensed matter
Lectures:
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"
References:
Books on many-body physics in general (occupation number formalism, Hubbard
model, Green function, self-energy, finite temperature formalism, Fermi
liquid theory) see, for example:
(i) Chapters 1,2,3,5,6 of J. W. Negele and H. Orland, "Quantum Many-Particle
Systems" (Addison-Wesley, 1988), or
(ii) Chapters 6,7,8,9,10 of P. Coleman, "Many_Body Physics",
http://www.physics.rutgers.edu/~coleman/mbody/pdf/bk.pdf
[2] Mean-field theories, the limit of high-dimensional lattices in
statistical physics, and the construction of DMFT:
(i) Chapters 1 and 4 of "Investigations of correlated electron systems using
the limit of high dimensions", by D. Vollhardt, see http://www.physik.uni-augsburg.de/theo3/Research/research_jerusalem.vollha.de.shtml
(ii) Dynamical mean-field theory of strongly correlated fermion systems and
the limit of infinite dimensions", A. Georges et al.; Rev. Mod. Phys.,
68,
13 (1996).
[3] LDA+DMFT:
"Realistic Investigations of correlated electron materials with LDA+DMFT",
K. Held et al., Psi-k Newsletter 56, 65 (2003), see http://www.psi-k.org/newsletters/News_56/Highlight_56.pdf
[4] Kinks:
"Kinks in the dispersion of strongly correlated electrons" K. Byczuk et al.;
Nature Physics 3, 168 (2007); see http://www.physik.uni-augsburg.de/theo3/Publications/bibliography/10.1038/nphys538-manuscript.pdf
[5] Disorder (Anderson localization):
"Localization Effects in Disordered Systems", D. Vollhardt, in
Festkoerperprobleme XXVII, Advances in Solid State Physics (Vieweg,
Wiesbaden, 1987), p. 63, see http://www.physik.uni-augsburg.de/theo3/Research/Localiz_effects-Festkoerperprob_1987.pdf
[6] Mott-Hubbard transition versus Anderson localization:
K. Byczuk, W. Hofstetter, and D. Vollhardt; Phys. Rev. Lett. 94, 056404 (2005); Phys. Rev. Lett. 102, 146403 (2009), see http://www.physik.uni-augsburg.de/theo3/Publications/bibliography/10.1103/PhysRevLett.102.146403.pdf
[7] Helium-3:
"Normal 3He: An Almost Localized Fermi-Liquid", D. Vollhardt, Rev. Mod.
Phys. 56, 99 (1984).
[8] Superfluid Helium-3:
"Superfluid Helium 3: Link between Condensed Matter Physics and Particle
Physics", D. Vollhardt and P. Woelfle, Acta Physica Polonica B 31, 2837
(2000), arXiv:cond-mat/0012052.