Condensed Matter Theory
Faculty
Research Areas
Condensed matter theory attempts
to describe and sometimes to predict the behavior of systems of relatively large numbers of particles (as many
as 1024 for bulk systems or as few as 1010 for two-dimensional layers, and as few as 102
for micelles) at low energies, typically far less than 0.1 eV. The variety of systems which are treated is extremely
rich, including metals and superconductors, ionic and magnetic systems, semiconductors, glasses and superfluids.
Condensed matter theorists also study the physical properties of soft condensed matter such as colloids, gels,
emulsions, micelles, foams, liquid crystals, polymer melts and biological systems. Soft Matter physics includes
phenomena ranging from the precise transition of liquid crystals to the lurches and shudders of sandpiles, from
the resilience of rubber to the self-organized structure of soft surfaces, and from neuromuscular twitch to single-molecule
mechanics. The basic tools of the condensed matter theorist are quantum mechanics and statistical mechanics as
well as many-body theory, path integrals, topology, group theory, density functional theory, computational physics
and so forth.
Condensed matter theory has evolved very rapidly in recent years. Before the late 1960's, condensed matter was
basically a semi-classical subject because of the surprising fact that electrons in metals and semiconductors behave
very much like non-interacting fermions. The justification for nearly-free-electron-like behavior was provided
by Landau's Fermi liquid theory which showed that, in many cases, interactions simply lead to renormalized band
parameters. More recently however, both experimental and theoretical interest has shifted to systems in which interaction
effects are overwhelming. Such systems include antiferromagnetic insulators which, according to band theory, should
be metals. They include systems with fluctuating valence states and heavy fermion systems in which electrons move
as if they had the mass of a proton. Recently understood phenomena such as strong and weak localization are also
not describable in terms of semi-classical theories. The integral and fractional quantum Hall effects are examples
of systems in which disorder and electron-electron interactions are inextricably interlinked, and the new high
temperature superconductors provide challenges which are likely to remain with us for many years.
For at least the past four decades there have continued to be close connections between the problems studied
by condensed matter theorists and those studied by particle theorists. For example, the concepts of spontaneously
broken symmetries and Goldstone's theorem arose first quite naturally in condensed matter theory. The renormalization
group, created by particle theorists, lay dormant for many years until it was resurrected by another particle theorist,
Ken Wilson, to solve the problem of the liquid-gas transition (as well as that of ferromagnetism, the Kondo problem
and a host of other problems in condensed matter physics). Subsequently, after these methods were fully developed
in the context of condensed matter theory, they were applied to other problems, such as lattice gauge theories
and confinement.
The reason why condensed matter theory is so important for other areas of theoretical physics is that it has
an extremely rich structure as does, for example, field theory, but it is free of divergences in both the ultraviolet
(because the size of an atom is not zero) and in the infrared (because the size of the sample is not infinite).
Also condensed matter systems are relatively easy to visualize, and hence frequently provide paradigms of subtle
concepts. For example, superconductivity provides the classic illustration of the Higgs mechanism in particle physics,
and more recently, the concept of fractional statistics, which interpolate between Bose and Fermi statistics, has
been realized in the fractional quantum Hall effect.
The condensed matter theory group at McMaster consists of five faculty members,
Drs. Berlinsky,
Carbotte,
Kallin,
Shi
and Sorensen.
This group works closely with our very active experimental groups in the areas
of high temperature superconductivity, low-dimensional systems, neutron scattering,
and the polymer scientists in the Chemistry, Biochemistry and Chemical Engineering
Departments. There is a strong interaction in polymer physics with Xerox Research
Centre of Canada located in Mississauga, about 30 km away from McMaster. This
group also makes extensive use of the state-of-the-art computer facilities associated
with SHARCNET