XII Training Course in the Physics of Strongly Correlated Systems
Vietri sul Mare (Salerno) Italy
1 - 12 October 2007
Lecture Topics and Background References
Prof. Stephan Haas
of Physics and Astronomy, University of Southern California (USA)
Magnetism, Nanomagnets and Entanglement
1. Independent Spins and Weiss Meanfield Theory
2. Finite Heisenberg Clusters
3. Spinwave Theory
4. Classical and Quantum Monte Carlo
5. Entanglement across Phase Transitions
1. numerical solution of meanfield equations, and geometry dependent meanfield treatment of nanoclusters.
2. numerical diagonalization of small Heisenberg clusters, effects of frustration.
3. real-space spinwave theory for nanoclusters
4. determination of scaling exponents from Monte Carlo
5. measures of entanglement in Heisenberg clusters
Prof. Mark Jarrell
Department of Physics, University of Cincinnati (USA)
Quantum Monte Carlo Methods for the Quantum Cluster Problem
1. Dynamical Mean Field and Dynamical Cluster Formalisms
2. The Hirsch-Fye Quantum Monte Carlo (QMC) cluster solver
3. Continuous time QMC cluster solver
4. The Maximum Entropy Method (MEM) (notes)
5. What can be done with Quantum Cluster Methods using QMC+MEM?
1. A blackboard discussion of the DMFA and DCA formalisms.
2. QMC tricks of the trade 1: Optimizing and parallelizing your QMC codes
3. QMC tricks of the trade 2: Optimizing and parallelizing your QMC codes
4. What can go wrong with a Maximum Entropy Calculation?, and how to fix it! (notes)
5. Beyond the DMFA/DCA: The Multi Scale Many Body method
1. Th. Maier, M. Jarrell, Th. Pruschke, and M. Hettler Quantum Cluster Theories, Reviews of Modern Physics, 77, pp. 1027-1080 (2005).
3. Bayesian Inference and the Analytic Continuation of Imaginary-Time Quantum Monte Carlo Data, M. Jarrell, and J.E. Gubernatis, Physics Reports Vol. 269 #3, pp133-195, (May, 1996).
MEM, DCA/QMC, etc) on my web page
1. I will post materials for the course (including detailed notes about
2. MEM, DMFA and DCA codes available online
MEM, DCA/QMC, etc) on my web page
Institut, Universität Karlsruhe (Germany)
1. General introduction to phase transitions
Overview over the course - Landau theory - Universality and scaling - dynamical critical behavior - New universality classes?
2. Fermi liquids and non-Fermi-liquid scenarios
Quasiparticle concept - Fermi-liquid properties - Kondo effect: local Fermi liquid - Heavy-fermion systems
3. Quantum phase transitions
Different types of quantum critical points - Hertz-Millis model - Quantum phase transitions in metals - Breakdown of the Hertz-Millis model - Local quantum criticality - Pomeranchuk instabilities
4. Ce-Cu-Au; a case study
Introduction to the system - Thermodynamic and transport properties - Measurement of critical fluctuations by inelastic neutron scattering - Role of the tuning parameter: compositon, hydrostatic pressure, magnetic field
5. Metal-insulator transitions in heavily doped semiconductors
Classification of metal-insulator transitions - Heavily doped semiconductors as ideal amorphous metals - Impurity-band states - electron interaction effects - Scaling properties of metal-insulator transitions
1. Low temperature thermodynamic and transport experiments
2. Elastic and inelastic neutron scattering
3. Disorder effects
4. Overview over different heavy-fermion systems
H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007)
of Physics, Zagreb (Croatia)
and charge transport in correlated thermoelectrics
I. Description of thermoelectric and thermomagnetic pheomena by irreversible thermodynamics. The approach to equilibrium, entropy increase and the flow of currents in response to generalized forces. Description of stationary currents by transport equations. Symmetry of kinetic coefficients and various relations connecting the coefficients of the energy current, the heat current, the entropy current, the particle and charge current. Solution of the transport equation and physical meaning of the thermoelectric coefficients. Efficiency of thermoelectric devices, thermocoolers, thermoelectric generators, and the figure-of-merit.
2. Quantum mechanical formulation of the heat and charge transport in homogenous systems. Current density operators of some typical many-body Hamiltonians, like Hubbard, Anderson and Falicov-Kimball Hamiltonian. Evaluation of the statistical averages of current operators, gradient expansion, and the derivation of the transport equations. Expressions for the transport coefficients in terms of the correlation functions of underlying microscopic models.
3. Relationship between the charge and energy current densities and the proof of the Mahan-Johnson theorem. Relationship between the current-current and the current - heat current correlation functions.
4. Thermoelectric properties of intermetallic compounds with Ce, Yb and Eu ions. Description of the anomalies revealed by the experimental data.
V. Heat and charge transport in inhomogenous thermoelectrics. Solution of
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