The physics of Strongly Correlated Systems is a central area of research in Condensed
Matter Physics. It is largely motivated by the problem of understanding High Temperature
Superconductivity. However it has many conceptual connections with other problems in
Condensed Matter such as the Quantum and Fractional Hall effects, Quantum Magnetism and
Quantum Critical Behavior, the physics of quasi-one-dimensional conductors and quantum
impurity systems. In this course I will discuss the main conceptual issues involved in the
physics of Strongly Correlated Systems, as well as their connections with these other
problems. This is an exciting area of research both in experiment and theory.
We have learned a lot in the past ten years. For instance, we now know that, unlike
conventional
superconductors, the high temperature superconductors have an order parameter with
d-wave symmetry. Also new and unexpected phenomena has been discovered such as the
existence of
stripe phases. However, although
many novel and interesting ideas have been proposed since the discovery of high temperature
superconductivity, we still do not have a complete theoretical understanding of this
phenomenon. In the past decade, however, we have gained
a solid understanding of the physics of these problems, and many of these ideas
have now become to coalesce into a coherent body of knowledge. The understanding of
these problems has also required the development of new theoretical tools, which are
not usually covered by the conventional graduate courses.
The purspose of this class is to introduce the main ideas in the physics of Strongly
Correlated Systems, to discuss what we understand of them, both in experiment and
theory, and their implications for current and future research in the field. I will assume
that the students have passed the Quantum Mechanics sequence (480-481) and the introductory
Solid State Physics course (489). Although field theoretic methods are often used in this
field, I will not assume that the student know quantum field theory (or many body physics
which is the same). Rather I will develop the technique as we go along and at the level
needed to understand the problem. The basic text for this class will be my book
Field Theories of Condensed Matter Systems, published by Addison-Wesley in 1991,
supplemented with additional material to cover topics not included there.