Condensed Matter Physics Seminar

Effective field theories that describe the dynamics of a conserved U(1)current in terms of "hydrodynamic" degrees of freedom of topological phases are discussed in general dimension D = d + 1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant, we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the theta (when D is even) terms. For topological insulators characterized by a Z2 topological invariant, their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.