**XVI
Training Course in the Physics of Strongly Correlated Systems**

*Vietri sul Mare (Salerno) Italy*

*October 3 -14, 2011*

*Lecture Topics and
Background References*

**Professor John A. Mydosh**

Kamerlingh Onnes Laboratorium and Lorentz-Instituut

Leiden Universiteit

Leiden

Netherlands

**Title: From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions**

Lectures will present a broad overview of the basic experimental phenomena and physical properties of the following topics:

1) Kondo effect, Ref. J.Phys.Soc.Jpn. 74, January 2005.

2) Spin glasses, Ref. J. A. Mydosh, Spin Glasses: An Experimental Introduction (London: Taylor and Francis, 1993).

3) Giant magnetoresistence, Ref. G. Binasch et. al., Phys.Rev.B 39, 4828(1989) and M. N. Baibich et al., Phys.Rev.Lett. 61, 2472(1988).

See also online Scientific Background on the Noble Prize in Physics and Noble Lectures –A. Fert and P. Grünberg, in Rev.Mod. Phys. 80, 1517 and 1531(2007).

4) Magnetoelectrics and multiferroics, Ref. M. Fiebig, J.Phys.D: Appl.Phys. 38, R123(2005), S-W. Cheong and M. Mostovoy, Nature Mater. 3, 13(2007), and R. Ramesh and N. A. Spalding, Nature Mater. 3, 21(2007).

5) High temperature superconductors, Ref. Y. Li, et al., Nature 455, 372(2008), ibid 468, 283(2010) and R-H He et al., Science 331, 1579 (2011).

6) Applications of superconductivity, Ref. G. W. Crabtree and D. R. Nelson in Physics Today, April 1997 and online brochure from American Superconductor – “Superconductor Power Cables”

7) Heavy fermions, Ref. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993), G. R. Steward, Rev.Mod.Phys. 78, 743(2006) and C. Pfleiderer, Rev.Mod.Phys. 81, 1551(2009).

8) Hidden order in URu2Si2, Ref. J. A. Mydosh and P. M. Oppeneer, Rev.Mod.Phys. 84, xxx(2011), arXiv:1107.0258.

9) Modern experimental methods in correlated electron systems, Ref. J. A. Mydosh and P. M. Oppeneer, Rev.Mod.Phys. 84, xxx(2011), arXiv:1107.0258

10) Quantum phase transitions, Ref. Subir Sachdev, Quantum Phase Transitions (Cambridge University Press, 2011), Second Edition.

**Professor Thomas Pruschke**

Institute for Theoretical Physics

University of Göttingen

Göttingen

Germany

**Title: Landau's Fermi Liquid Concept to the Extreme: the Physics of Heavy Fermions**

**Tentative lecture titles:**

Monday, October 10th |
2h |
Repititorium – The free electron gas |

Tuesday, October 11th |
1h |
Landau’s Fermi Liquid Theory part I |

Wednesday, October 12th |
2h |
Landau’s Fermi Liquid Theory part II |

Thursday, October 13th |
1h |
Heavy Fermions part I |

Friday, October 14th |
4h |
Heavy Fermions part II |

**References and suggested Reading:**

- Ashcroft and Mermin,
*Solid State Physics* - Nozières and Pines,
*Theory Of Quantum Liquids* - Hewson,
*The Kondo Problem to Heavy Fermion* - Mahan,
*Many-Particle Physics* - Stewart,
*Heavy Fermion Systems*, Rev. Mod. Phys. 1984 - Georges et al.,
*Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions*, Rev. Mod. Phys. 1996 - Bulla et al.,
*The numerical renormalization group method for quantum impurity systems*, Rev. Mod. Phys. 2008

**Intended Problem assignments:**

Monday, October 10th: Physical quantities for the free electron gas (analytical)

Tuesday, October 11th: Anderson and Kondo model – basic properties (analytical)

Wednesday, October 12th: Dynamical mean-field theory with NRG – basic ideas and how to use it (numerical, code provided)

Thursday, October 13th: Dynamical mean-field theory with NRG – application to heavy fermion models (numerical, code provided)** **

** **

** **

**Professor Ulrich Schollwöck**

Department für Physik

Ludwig-Maximilians-Universität München

München

Germany

**Title: Simulations using matrix product states**

Lectures:

1) Matrix product states I

- why are strongly correlated quantum states difficult?

- introduction to entanglement theory

- representing states as matrix product states

- overlaps/expectation values in MPS

2) Matrix product states II

- orthonormalizing matrix product states

- compressing matrix product states

- general properties of correlations in matrix product states

3) Real and imaginary time-evolutions using matrix product states

- Trotter decompositions

- imaginary time-evolution for ground states

- real time-evolution for quench dynamics

4) Variational ground state searches with matrix product states

- Matrix product operators

- Variational search methods

5) Outlook

- connections to the Numerical Renormalization Group

- extending the range of time-dependent simulations

- going towards two dimensions

References:

There exist several reviews, which cover the topic of the lectures quite well and in some detail. Students can follow up from those to the original references, which however are often quite arcane.

1) U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)

2) U. Schollwöck, Ann. Phys. 326, 96 (2011)

3) F. Verstraete, V. Murg, J.I. Cirac, Adv. Phys. 57, 143 (2008)

The lectures will follow the notation and spirit of 2), but also take from 1) and 3). 3) gives a more quantum information based perspective, 1) is "old-fashioned" in the sense that matrix product states do not figure very prominently, but it makes more of a connection to a statistical physics perspective (more DMRG like, as in previous Vietri courses). Reading Noack/Manmana and Feiguin in earlier Vietri books could also be helpful, but is not necessary.

Problem classes:

1) Exact diagonalization (Lanczos) - programming

Decomposition of states as MPS - programming

Calculating entanglement of simple states - analyt.

2) The AKLT model as the simplest non trivial MPS

Constructing the MPS of the AKLT model - analyt.

Calculating its correlators - analyt.

3) Working out Trotter decompositions of simple Hamiltonians - analytical, programming

Orthonormalize and compress MPS - programming

4) Time-evolutions with MPS - programming

**Professor David Singh**

Oak Ridge National Laboratory

Oak Ridge TN

USA

**Title: The Solid State as a Fabric for Intertwining Chemical Bonding, Electronic Structure and Magnetism**

Lectures:

1: “First Principles Calculations: The Glue that Binds Materials and Models”

General introduction to density functional theory, approaches and some words about applications of density functional theory. Also a brief introduction to the LAPW method, which would be helpful for the afternoon session.

2: “The Wacky World of Perovskites”

Some of the physics observed in perovskites emphasizing mostly structure and its interplay with properties. Also ferroelectricity.

3: “Magnetism and Superconductivity”

This is about unconventional superconductors, especially the interplay of magnetism with the Fermi surface and what can be learned from first principles. The examples will be ruthenates and iron-pnictides, but other materials will be mentioned as well.

4: “Thermoelectrics: Getting a Grip on Heat”

The basics of thermoelectric materials are discussed along with Boltzmann transport theory as may be applied from first principles band structures.

5: “Electronic Structure and Chemical Bonding”

This is about the interplay of electronic structure and bonding using various examples. It is also intended as an opportunity for students to participate.

Training sessions:

Brief introduction to the LAPW method (if not in the morning) and hands on with the ELK code.