Condensed Matter Seminar - Juerg Froehlich, ETH Zurich & IAS, Princeton - Gauge Theory and Topological Phases of Matter

Mon, Feb 25, 2013, 1:15 pm to 2:30 pm
PCTS Seminar Room
We study a general class of systems of condensed matter including electron liquids and atom gases. Thanks to the U(1)- and SU(2)- gauge invariance of the quantum theory of such systems, one may study their response to coupling the electric current to a vector potential and the spin current to an SU(2)- gauge field. Response equations are found by determining their effective actions (or free energies) as functionals of the U(1)-vector potential and SU(2)-gauge field (and of the metric of the sample). The physical interpretation of these fields is explained. Using only general principles – gauge invariance, cluster properties of connected (current) Green functions in systems with a mobility gap, power counting – the form of the effective actions is determined. This leads to a “gauge theory of phases of matter” complementary to the well-known Landau theory. Applications to systems exhibiting the quantum Hall and the spin Hall effect, to 3D topological insulators, and to the primordial plasma in the universe are discussed.