VI Training Course in the Physics of

Correlated Electron Systems and High-Tc Superconductors


Vietri sul Mare (Salerno) Italy

8 - 19 October 2001


Lecture Topics and Background References



Prof. P. Coleman

Dept of Physics and Astronomy, Rutgers University

Local moment physics and quantum criticality



1) Local moment formation in atoms and quantum dots.

2) The Kondo problem.

3) Mean-field approach to the Kondo lattice.

4) Quantum criticality and open questions.


General Reviews:

Scaling approach to Kondo model: P. Nozieres and A. Blandin, J. Physique 41, 193 (1980).

Physics of Heavy Fermion materials: G. Stewart, RMP 56, 755 (1984).

General Text on Kondo and Anderson physics: A. Hewson, Kondo model to heavy fermions, (Cambridge University Press, 1993) [Chapters: 1, 3, 5, 7/8, 10].

Quantum Criticality: S. Sachdev, Quantum Phase Transitions, (Cambridge University Press, 1999) [Chap. 12, pp. 234].

Current situation with Quantum Criticality: P. Coleman, C. Pepin, Q. Si and R. Ramazashvili, Journal of Physics: Condensed Matter 13, 723 (2001) [cond-mat/0105006].

Quantum Dots: L. Kouwenhoven and L. Glazman, The revival of the Kondo effect, Physics World 14, 33 (???) [cond-mat/0104100].


More detailed papers:

Local moment formation: P.W. Anderson, PR 124, 41 (1961).

Poor Man Scaling: P.W. Anderson, Journal of Physics C 3, 2436 (1970).

Schrieffer-Wolff Transformation: J.R. Schrieffer and P. Wolff, PR 149, 491 (1966); B. Coqblin and J.R. Schrieffer, PR 185, 847 (1969).

Kondo lattice concept: S. Doniach, Physica B 91, 231 (1977).

Slave bosons and large N approach: P. Coleman, PRB 35, 5072 (1987); P. Coleman, PRB 28, 5255 (1983).

Kondo/Anderson Lattice: A.J. Millis and P.A. Lee, PRB 35, 3394 (1986); A. Auerbach and K. Levin, PRL 57, 877 (1986).

Quantum Criticality: J.A. Hertz, PRB 14, 1165 (1976); A.J. Millis, PRB 48, 7183 (1993).




Prof. C. Di Castro

Dipartimento di Fisica, UniversitÓ degli Studi di Roma "La Sapienza"

Symmetry properties, Ward identities and renormalization group for Fermi and Bose systems

Bose liquid. Luttinger liquid and high Tc superconductivity




S. Caprara, and C. Di Castro, Int. J. Mod. Phys. A 16, 2015 (2001)

C. Di Castro, M. Grilli, and S. Caprara, cond-mat/0109319 and references therein






Prof. P. Prelovsek

J. Stefan Institute, Department of Theoretical Physics, University of Ljubljana

Transport in strongly correlated systems



1) Transport and integrabilility

Charge stiffness at T=0: conductors (metals) vs. insulators. Charge stiffness at T>0 - relation to level dynamics. 1D Integrable systems -ideal conductors, ideal insulators. Conserved quantities in integrable systems. Generic nonintegrable systems.

2) Numerical methods and results for dynamical conductivity

Lanczos algorithm for the ground state energy and dynamics. Finite-temperature Lanczos method. Conductivity in planar strongly correlated models: relation to experiments in cuprates.

3) Hall response in correlated systems

Anomalous Hall response in cuprates. T=0 Hall constant in a ladder geometry. Reactive Hall constant in a slow limit: relation to charge stiffness. T=0 Hall constant in the transport limit. Hall response at T>0: analytical and numerical results.



W. Kohn, Phys. Rev. 133, A171 (1964)

H. Castella, X. Zotos, and P. Prelovsek, PRL 74, 972 (1995)

X. Zotos, and P. Prelovsek, PRB 53, 983 (1996)

X. Zotos, F. Naef and P. Prelovsek, PRB 55, 11029 (1997)

J. Jaklic and P. Prelovsek, PRB 49, 5065 (1994)

J. Jaklic and P. Prelovsek, Adv. in Phys. 49, 1 (2000)

P. Prelovsek, M. Long, T. Markez, and X. Zotos, PRL 83, 2785 (1999)

X. Zotos, F. Naef, M. Long, and P. Prelovsek, PRL 85, 377 (2000)

P. Prelovsek and X. Zotos, cond-mat/0107247






Prof. C.M. Varma

Bell Laboratories, Lucent Technologies

Singular Fermi Liquids



1) Introduction

2) Landau's Fermi-liquid

3) Local Fermi-Liquids & Local Singular Fermi-Liquids

4) SFL behavior for interacting fermions in one dimension

5) Singular Fermi-liquid behavior due to gauge fields

6) Quantum Critical Points in fermionic systems

7) The High-Tc Problem in the Copper-Oxide Based Compounds

8) The Metallic State in Two-Dimensions



C.M. Varma, Z. Nussinov and Wim van Saarloos, cond-mat/0103393



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