XII Training Course in the Physics of Strongly Correlated Systems
Vietri sul Mare (Salerno) Italy
1 - 12 October 2007
Lecture Topics and Background References
Department
of Physics and Astronomy, University of Southern California (USA)
Quantum
Magnetism, Nanomagnets and Entanglement
Lectures:
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
Tutorials:
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
References
http://physics1.usc.edu/~shaas/PHYS-640(Haas).pdf
Department of Physics, University of Cincinnati (USA)
Quantum Monte Carlo Methods for the Quantum Cluster Problem
Lectures:
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?
Tutorials:
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
References:
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).
Useful Links:
1. I will post materials for the
course (including detailed notes about
2. MEM, DMFA and DCA codes
available online
Physikalisches
Institut, Universität Karlsruhe (Germany)
Quantum
phase transitions
Lectures:
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
Tutorials:
1.
Low temperature thermodynamic and transport experiments
2.
Elastic and inelastic neutron scattering
3.
Disorder effects
4.
Overview over different heavy-fermion systems
Reference
H.
v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Fermi-liquid instabilities at
magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007)
Institut
of Physics, Zagreb (Croatia)
Heat
and charge transport in correlated thermoelectrics
Lectures:
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
References:
H. B. Callen, Phys. Rev. 73, 1349 (1949).
C. A. Domenicali, Rev.
Mod.Phys. 16, 237 (1954). Oxford,
1984).
E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii,
Electrodynamics of Continuous Media (Elsevier Butterworth-Heinemann, 1984).
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).
