September 21, 2015 – September 25, 2015

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Location

Forschungszentrum, Julich

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Organizers

Eva Pavarini, Forschungszentrum Jülich
Eric Koch, Forschungszentrum Jülich
Piers Coleman, Rutgers University

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Overview

Many-body physics has the daunting task of describing the collective behavior of vast assemblies of elementary objects. While the fundamental laws are known, exact solutions like the Bethe Ansatz are exceedingly rare. Nonetheless, the past century has witnessed a continuous stream of conceptual breakthroughs, prompted by unforeseen discoveries of new states of matter: superconductivity and superfluidity, antiferromagnetism, the Kondo effect, the Mott transition, symmetry breaking, spin glasses and frustration, heavy Fermions and high-temperature superconductivity. Each of these cooperative phenomena is an example of emergence at work. Their essence can often be captured by simple model Hamiltonians. Describing the richness of real matter requires, however, to increase the complexity of the models significantly, as emergent phenomena are frequently governed by the interplay of several scales. In this year’s school we will highlight the Kondo effect, the physics of the Hubbard model, and frustrated quantum spins, covering the range from fundamental mechanisms to the modeling of real materials. The aim of the school is to introduce advanced graduate students and up to the essence of emergence and modern approaches for modeling strongly correlated matter. 

The school will prepare the next generation of researchers for advancing the understanding of strong correlations in the solid state. For this, students need a broad background on complementary techniques ranging from traditional density-functional methods to advanced many-body theories. They also need a deep understanding of many-body phenomena such as the Kondo effect, correlated magnetism, spin-frustration, superconductivity and the Mott transition. Such a background comes from a range of different established and well separated areas of condensed-matter research, and is thus difficult to build into conventional curricula. To further advance the field, the next generation of students needs to work at the interface of all these research areas and must be able to judge works in all subjects involved. The present school aims at advancing the students to the frontiers of research, through a set of comprehensive and pedagogical lectures which cover the essential aspects. The school offers the unique chance of discussing open problems from many perspectives, ranging from ab-initio approaches to the hard many-body aspects. 

The school is built around the challenge of understanding strong correlation phenomena in condensed matter, which will be presented already on the first day. The discussion of open questions will be continued in the course of the school; open problems will be addressed in several of the more advanced lectures, as well as during the ample discussion times. Students will be prepared to identify the important unsolved problems as well as the common issues in strongly correlated systems opening up to new ideas and novel research directions. 

Lecture Topics:

• Heavy-fermions and Kondo systems.

• Spin frustration phenomena.

• Mott transition.

• Hybrid functionals.

• The Bethe Ansatz approach.

• Poor’s man scaling.

• Numerical renormalization Group method (fermions and bosons).

• Variational methods.

• Quantum Cluster methods.

• Dynamical Cluster Approximation.

• Slave bosons theory.

• Numerical methods for correlated spin systems.

• Spin glasses.

• Hubbard model.

• Anderson model.