Lecture Topics and Background References

XIV Training Course in the Physics of Strongly Correlated Systems

Vietri sul Mare (Salerno) Italy

5 - 16 October 2009

Lecture Topics and Background References

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:

K. Held , I. A. Nekrasov , G. Keller , V. Eyert , N. Blümer , A. K. McMahan , R. T. Scalettar , Th. Pruschke , V. I. Anisimov , D. Vollhardt, Realistic investigations of correlated electron systems with LDA + DMFT, physica status solidi (b), 243, 2599 (2006).
Electronic Structure Calculations using Dynamical Mean Field Theory, K. Held, Adv. Phys. 56, 829 (2007), arXiv:cond-mat/0511293.
V. I. Anisimov, D. E. Kondakov, A. V. Kozhevnikov, I. A. Nekrasov, Z. V. Pchelkina, J. W. Allen, S.-K. Mo, H.-D. Kim, P. Metcalf, S. Suga, A. Sekiyama, G. Keller, I. Leonov, X. Ren, and D. Vollhardt, Full orbital calculation scheme for materials with strongly correlated electrons, Phys. Rev. 71, 125119 (2005).
Edited by Vladimir Anisimov, “Strong Coulomb Correlations in Electronic Structure Calculations”, Gordon and Breach Science Publishers, 2000.
V.I.Anisimov, F.Aryasetiawan, A.I.Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method, J.Phys.: Condens. Matter 9, 767 (1997).

Professor Anders W. Sandvik

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).

Professor George Sawatzky

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.

Professor Dieter Vollhardt

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
[1] Introduction to electronic correlations, dynamical mean-field theory (DMFT) and LDA+DMFT:
"Strongly Correlated Materials: Insights from Dynamical Mean-Field Theory", G. Kotliar and D. Vollhardt, Physics Today 57, 53 (2004), see http://www.physik.uni-augsburg.de/theo3/Publications/PT-Kotliar0304.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.