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Karsten Held: Dynamical Mean Field Theory

Dynamical mean field theory has led to recent advances
in our understanding of electronic correlations in model
Hamiltonians and the Mott-Hubbard metal-insulator
transition in particular.
I will give an introduction to DMFT and discuss the DMFT
findings for the Mott-Hubbard transition, including recent
electronic structure calculations for V2O3.
These new developments and results call for a better
mathematical foundation, and I will point out where
mathematical physicists can contribute.


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Andre-Marie Tremblay: The Two-Particle Selcf Consistent Approach

1. Destruction of the Fermi surface: 
Confronting Theory, Experiment and Simulations

Abstract
This first talk will be at an elementary level and will make heavy use of
images. I will motivate the need for development of new methods for
interacting electrons by showing the results of experiments and of
corresponding theoretical calculations for high-temperature
superconductors near their parent insulating phases. Like many other
strongly correlated systems, even in their normal phase these systems do
not behave like standard Many-Body Theory would predict. Many probes, and
especially photoemission, reveal that the Fermi surface is destroyed, or
equivalently that there exists a "pseudogap". Starting from the Hubbard
model, I will argue that there is a weak-coupling way to create a
pseudogap that is much better understood than the strong-coupling way and
that applies to electron-doped high-temperature superconductors near
optimal doping. For these cuprates, our theoretical calculations using
TPSC on the Hubbard model are in remarkable agreement with photoemission
and neutron experiments. These calculations are based on the Two-Particle
Self-Consistent approach (TPSC). I will discuss the advantages of this
approach over other Many-Body schemes and argue that comparisons with
Quantum Monte Carlo simulations show that TPSC is more reliable than other
approaches. I will also mention a number of predictions of TPSC for
experiment as well as what is has to say on d-wave superconductivity.

Short bibliography:

D. Sénéchal and A.-M.S. Tremblay,
"Hot Spots and Pseudogaps for Hole- and Electron-Doped High Temperature
Superconductors"
Phys. Rev. Lett. 92, 126401/1-4 (2004). (4 pages)

B. Kyung, V. Hankevych, A.-M. Dare and A.-M.S. Tremblay,.
"Pseudogap and Spin Fluctuations in the Normal State of Electron-Doped
Cuprates"
Submitted Phys. Rev. Lett.. cond-mat/0312499 (4 pages)

B. Kyung, J.S. Landry and A.-M.S. Tremblay
"Antiferromagnetic fluctuations and d-wave superconductivity in
electron-doped high-temperature superconductors"
Phys. Rev. B 68, 174502/1-5 (2003) (5 pages).

S. Moukouri, S. Allen, F. Lemay, B. Kyung, D. Poulin, Y.M. Vilk and
A.-M. S. Tremblay
"Many-body Theory vs Simulations for the pseudogap in the Hubbard model"
Phys. Rev. B 61, 7887-7892 (2000) (6 pages).

Y.M. Vilk and A.-M.S. Tremblay,
"Non-perturbative approach to the Hubbard model and single-particle
pseudogap"
J. Phys. I France 7, 1309-1368 (1997). (60 pages)

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2. Formal issues in Many-Body Theory and where the
Two-Particle-Self-Consistent Approach fits.

Abstract
In the first part of this talk I will present a short phenomenological
derivation of the Two-Particle Self-Consistent Approach (TPSC). In the
second part I will introduce the conserving approximation scheme to
many-body problems that was developed by Kadanoff and Baym within the
Schwinger-Martin functional-derivative approach. TPSC also satisfies
conservation laws, but in addition it satisfies the Pauli principle, a
number of sum rules as well as a consistency check involving a relation
between one and two-particle properties. A concise formal derivation of
that approach, using functional derivatives, will be given to highlight
formal analogies and differences with conserving approximations. This
general scheme can also be applied to the attractive Hubbard model and in
some cases can be generalized to more complicated Hamiltonians. Results
for ferromagnetism as well as open problems will be mentioned.

Short bibliography:

S. Allen, A.-M.S. Tremblay, and Y.M. Vilk
"Conserving approximations vs Two-Particle Self-Consistent Approach" in
"Theoretical Methods for Strongly Correlated Electrons"
David Sénéchal, André-Marie Tremblay and Claude Bourbonnais (eds.)
CRM Series in Mathematical Physics, (Springer, New York, 2003), p.341-355
(15 pages)

S. Allen, and A.-M. S. Tremblay
"Non-perturbative approach to the attractive Hubbard model"
Phys. Rev. B 64, 075115/1-14 (2001) (14 pages).

V. Hankevych, B. Kyung, and A.-M.S. Tremblay
"Weak ferromagnetism and other instabilities of the two-dimensional t-t'
Hubbard model at Van Hove fillings"
Phys. Rev. B 68, 214405/1-11 (2003) (11 pages).