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

Department of Physics and Astronomy, University of Southern California (USA)

Quantum 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).
2. M . Jarrell, Th. Maier, C. Huscroft, and S. Moukouri, A Quantum Monte Carlo Algorithm for Non-local Corrections to the Dynamical Mean-Field Approximation, Phys. Rev. B 64, 195130/1-23 (2001).
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).
4. A .N. Rubtsov, Continuous-time quantum Monte Carlo for fermions, PRB 72 035122 (2005)
5. F . Assaad, Diagrammatic Determinantal methods: projective schemes and applications to the Hubbard-Holstein model, cond-mat/0702455v1

Useful Links:
1. I will post materials for the course (including detailed notes about MEM, DCA/QMC, etc) on my web page at http://www.physics.uc.edu/~jarrell/Salerno
2. MEM, DMFA and DCA codes available online http://www.physics.uc.edu/~jarrell/LINUX.html


  Professor Hilbert v. Löhneysen

Physikalisches Institut, Universität Karlsruhe (Germany)

Quantum phase transitions

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)



  Professor Veljko Zlatic

Institut of Physics, Zagreb (Croatia) 

Heat 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. Vertex corrections, analytic continuation, and the DMFT simplification. Evaluation of the correlation functions for some typical models of strong correlations.
4. Thermoelectric properties of intermetallic compounds with Ce, Yb and Eu ions. Description of the anomalies revealed by the experimental data. Characteristic energy scales revealed by the pressure and doping data. Explanation of pressure and doping effects on thermal transport of 4f ions by the periodic Anderson model with crystal field splitting. Characteristic energy scales of the model. Quasi-particle description of thermal transport in the coherent regime.  Derivation of the Fermi liquid laws and the universal low-temperature ratios (Kadowaki-Woods ratio, q-ratio, Wilson ratio).  Break-down of the Fermi liquid laws. Description of various routes leading to the high-temperature paramagnetic (high-entropy) phase. Poor man's solution' of the lattice problem at elevated temperatures.
V. Heat and charge transport in inhomogenous thermoelectrics. Solution of 1-dimensional boundary value problem for segmented thermoelectrics. Domenicali equation, figure-of-merit, coefficient of performance. Description of correlated multilayers by Falicov-Kimbal and Anderson models. Real-space formulation of thermoelectric coefficients and the solution of transport equation for corelated multilayers.


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C. A. Domenicali, Rev. Mod.Phys. 16, 237 (1954). Oxford, 1984).
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J. M. Luttinger, Phys. Rev. 135, A1505 (1964).
G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).
G. D. Mahan, in Solid State Physics, (Academic Press, 1998), Vol. 51, p. 81.
J. K. Freericks and V. Zlatic, Rev. Mod. Phys. 75, 1333 (2003).
J. K. Freericks and V. Zlatic, Phys. Rev. B 64, 245118 (2001).
V. Zlatic and R. Monnier, Phys. Rev. B 71, 165109 (2005).
V. Zlatic, R. Monnier, J. Freericks, and K. W. Becker, Phys Rev. B76, (2007).
J. K. Freericks, V. Zlatic; and A. M. Shvaika, Phys.Rev.B75, 035133 (2007).
J. Freericks and V. Zlatic, Phys. Stat. Solidi 244, 2351 (2007).


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