XIII Training Course in the Physics of Strongly Correlated Systems


Vietri sul Mare (Salerno) Italy

6 - 17 October 2008


Lecture Topics and Background References


Professor Gabriel Aeppli

Department of Physics and Astronomy, University College London, United Kingdom

Quantum magnetism in insulators


1. Single impurities in semiconductors and insulators - analogies with atomic physics, hyperfine interactions, and free electron laser
2. 1-dimensional magnets, including direct evidence for fermionic quasiparticles in antiferromagnetic S=1/2 chains, and quantum phase coherence and edge states in S=1 chains.
3. 2-dimensional magnets, including entanglement at short distances
4. 3-dimensional magnets - quantum phase transition, decoherence due to coupling to nuclear spin bath
5. Undoped and doped Kondo insulators

Journal club

General Background: “What Happens to Ordered Moments When They are no Longer Ordered?”, G. Aeppli, Physica B, 318, p. 5-11, (2002). “Seeing the Spins in Solids”, G. Aeppli, S. Hayden, T. Perring, Physics World, p. 33-37, (December 1997)
1. "Silicon as a model ion trap: Time domain measurements of donor Rydberg states” N. Q. Vinh, P. T. Greenland, K. Litvinenko, B. Redlich, A. F. G. van der Meer, S. A. Lynch, M. Warner, A. M. Stoneham, G. Aeppli, D. J. Paul, C. R. Pidgeon, B. N. Murdin PNAS 105 10649-10653 (2008)
2. “Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S = ½ Antiferromagnet”, D. C. Dender, P. R. Hammar, D. H. Reich, C. Broholm, G. Aeppli, Phys. Rev. Lett. 79(9), p. 1750-1753, (1997). “Mesoscopic Phase Coherence in a Quantum Spin Fluid” Guangyong Xu, C. Broholm, Yeong-AhSoh, G. Aeppli, J. F. DiTusa, Ying Chen, M. Kenzelmann, C. D. Frost, T. Ito, K. Oka, H. Takagi Science 317, p. 1049–1052 (2007)
3. “Quantum dynamics and entanglement of spins on a square lattice” N. B. Christensen, H. M. Rønnow, D. F.McMorrow, A. Harrison, T. G. Perring, M. Enderle, R. Coldea, L. P. Regnault, G. Aeppli PNAS 104 15264-15269 (2007)
4. "Quantum Critical Behavior for a Model Magnet”, D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), p. 940-943, (1996). “Tunable Quantum Tunneling of Magnetic Domain Walls” J. Brooke, T. F. Rosenbaum, G. Aeppli, Nature 413, p. 610 - 613 (2001). “Quantum phase transition in a spin bath”, H. M. Ronnow, R. Parthasarathy, J. Jensen, G. Aeppli, T. F. Rosenbaum, and D. F. McMorrow, Science 308, p. 392-395 (2005)
5. "Kondo Insulators", G. Aeppli, Z. Fisk, Comments Cond. Matt. Phys. 16, p. 155, (1992). "Unconventional Charge Gap Formation in Cubic FeSi", Z. Schlesinger, Z. Fisk, Hai-Tao Zhang, B. Maple, J. F. DiTusa and G. Aeppli, Phys. Rev. Lett. 71, p. 1748, (1993). “Magnetoresistance from Quantum Interference Effects in Ferromagnets”, N. Manyala, Y. Sidis, J. F. Ditusa, G. Aeppli, D. P. Young, Z. Fisk, Nature 404, p. 581-584, (2000). “Doping a semiconductor to create an unconventional metal” N. Manyala, J.F. DiTusa, G.Aeppli, A.P.Ramirez Nature 454 976–980 (2008)



Professor Peter Littlewood

Department of Physics, University of Cambridge, United Kingdom

Novel quantum condensates in excitonic matter


This course will interleave discussion of a novel physical problem of a new kind of Bose-Einstein condensate with teaching of the fundamental theoretical tools of quantum condensed matter field theory.

1. Introduction to the physical systems. The electron-hole gas, excitonic insulator; exciton-photon interactions, polaritons and the Dicke Model; exciton and polariton BEC.
2. Theoretical tools: Second quantization. Coherent states. Coherent state path integral. Examples of coherent state mean field theories: Dilute Bose gas. BCS superconductivity.
3. Exciton and polariton condensates in mean field theory. Field theory of polariton condensate; BEC-BCS crossover.
4. Theoretical Tools: Open systems and Keldysh formulation. Pair-breaking and the semiconductor laser.
5. Phase-breaking and open system dynamics. Review of experiment. Open questions and new systems.

Journal club

The methodological aspects are covered in standard quantum field theory texts: Professor Littlewood's approach will be closest to the book of Altland and Simons [1]. A recent theoretically focussed review of polariton systems is [2].
1. A. Altland, and B.D. Simons; Condensed Matter Field Theory; Cambridge University Press (2006).
2. J. Keeling, F.M. Marchetti, M.H. Szymanska, and P.B. Littlewood; Collective coherence in planar semiconductor microcavities; Semiconductor Science and Technology 22, R1 (2007).


  Professor Manfred Sigrist

Institut für Theoretische Physik, ETH Zürich, Switzerland

Introduction to Unconventional Superconductivity

1. Generalized BCS Theory.
2. Phenomenological Approach and Symmetry Aspects.
3. Josephson and Tunneling Effects.
4. Case Studies I.
5. Case Studies II.

1. Generalized BCS Theory: Bogolyubov-transformation and self-consistent equations.
2. Generalize Ginzburg-Landau Theory: Free energy and phases of a two-component order parameter.
3. Generalize Ginzburg-Landau Theory: Boundary properties of time reversal symmetry breaking phase.
4. High-Tc-superconductivity: Simple model of an RVB state.

1. V.P. Mineev, and K.V. Samokhin; Introduction to Unconventional Superconductivity; Gordon & Breach Publisher (1998).
2. M. Sigrist, and K. Ueda; Phenomenological Theory of Unconventional Superconductivity; Rev. Mod. Phys. 63, 239 (1991).
3. M. Sigrist; Introduction to Unconventional Superconductivity; AIP Conference Proceedings 789, 165 (2005).



  Professor Matthias Troyer

Institut für Theoretische Physik, ETH Zürich, Switzerland

Quantum Monte Carlo methods


1. Introduction to Monte Carlo simulations.
2. Classical and quantum cluster algorithms.
3. The worm algorithm.
4. Optimized ensembles for classical and quantum Monte Carlo simulations.
5. Continuous time QMC solvers for quantum impurity problems and DMFT.


ALPS Monte Carlo codes

1. D.P. Landau, and K. Binder; A Guide to Monte Carlo Simulations in Statistical Physics; Cambridge University Press (2005).
2. R.H. Swendsen, and J.-S. Wang; Phys. Rev. Lett. 58, 86 (1987). H.G. Evertz; Adv. Phys. 52, 1 (2003).
3. N.V. Prokof'ev et al.; Sov. Phys. - JETP 87, 310 (1998). A.W. Sandvik; Phys. Rev. B 59, 14157 (1999). O.F. Syljuasen, and A.W. Sandvik; Phys. Rev. E 66, 046701 (2002). F. Alet et al.; Phys. Rev. E 71, 036706 (2005).
4. F. Wang, and D.P. Landau; Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E 64, 056101 (2001). M. Troyer et al.; Phys. Rev. Lett. 90, 120201 (2003). S. Trebst et al.; Phys. Rev. E 70, 046701 (2004). S. Wessel et al.; J. Stat. Mech. P12005 (2007).

5. A.N. Rubtsov; Phys. Rev. B 72 035122 (2005). P. Werner et al.; Phys.  Rev. Lett. 97, 076405 (2006). P. Werner et al.; Phys. Rev. B 74, 155107 (2006). E. Gull et al.; Europhysics Letters 82, 57003 (2008).


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