Physics Dept., University of British Columbia

The CAP-CRM prize in theoretical physics is presented to Dr. Ian Affleck of the University of British Columbia for his very successful work in theoretical condensed matter physics highlighting field-theoretic methods and related mathematical physics.

In the 1970's and the early 1980's, most applications of field theory to critical phenomena were devoted to classical systems, mainly through renormalisation-group methods. Dr. Affleck has been one of the first physicists to systematically apply quantum field theory methods to the more subtle problem of quantum critical phenomena, focusing mainly on one-dimensional systems. On this subject he made important contributions in the period 1985-89. For instance, he proposed that Wess-Zumino-Witten models are the fixed points governing quantum spin chains. He also related this description of spin chains with the large-spin approximation based on the nonlinear sigma model. [Wess-Zumino-Witten models are two-dimensional quantum field theories with Lie group symmetry; they can be regarded as the building blocks of all two-dimensional quantum field theories having conformal invariance.] He also made significant contributions to the physics of quasi-one-dimensional spin-1 antiferromagnets in relation with the Haldane gap. Some of his discoveries in the area of quantum spin chains are now standard material in theoretical physics. The essentials of his results and insights were reported in the remarkable lectures presented at Les Houches in 1988, which became an influential review paper.

In 1990, in collaboration with A. Ludwig, he initiated a very important research program on the applications of the recently discovered boundary conformal field theory (formulated by Cardy) to various one-dimensional quantum impurity problems. These applications are mainly in condensed matter physics (e.g., the Kondo effect and its multi-channel and higher-spin generalizations, quantum wires, etc.) but some are related to particle physics and cosmology (the Callan-Rubakov effect describing baryon scattering off monopoles). Conformal field theory provides numerous examples of exactly solvable models (i.e, of which all correlation functions can be calculated exactly). However, apart from two-point functions from which critical exponents may be extracted, very little can be compared with experiments. In their approach to quantum impurities problems, Affleck and Ludwig have shown that various physical quantities (resistivity, specific heat, etc.) can indeed be calculated and compared with experimental data. These studies, in turn, have stimulated new experimental work, which further demonstrates the impact of Dr. Affleck's work. Moreover, this work often provides striking and original physical realizations of some of the most abstract constructions of conformal field theory, such as fusion rules or conformal embeddings in the treatment of the multi-channel Kondo effect.

Although Dr. Affleck's main focus has been the application of field theory methods to condensed matter physics, he has to his credit two fundamental discoveries in conformal field theory. One is the interpretation of the conformal anomaly the basic parameter of a conformal theory as a finite-size or Casimir effect. (The same result was found independently by Blöte, Cardy and Nightingale.) The second one, obtained in collaboration with Ludwig, is the discovery of the g-function, the "ground-state degeneracy", a measure of the impurity entropy, which has been shown to be always decreasing under renormalisation (in close analogy with the Zamolodchikov ctheorem). The importance of both contributions has been widely acknowledged.

Dr. Affleck joined UBC in 1987 as professor and fellow of the CIAR Cosmology Program. He is now also an associate of the CIAR Superconductivity Program. He graduated from Trent University in 1975 and obtained his Ph.D from Harvard University in 1979. He was junior fellow of the Harvard Society of Fellows from 1979 to 1981 and then associate professor at Princeton University until 1987. He received various distinctions since his arrival at UBC: Steacie Prize in 1988, the CAP Herzberg Medal in 1989, elected Fellow of the Royal Society of Canada in 1991, Rutherford Medal of the Royal Society of Canada in 1991, UBC Senior Killam Research Prize and UBC Jacob Bieley Prize in 1992.

The above text by Pierre Mathieu (Université Laval) is taken from Physics in Canada, July/August 1997.