Nonabelian Hall conductance in general dimensions as an invariant of the interacting ground state wavefunction

Abstract: The long-wavelength response of a gapped many-body system in D spatial dimensions with a Lie group symmetry G to an external gauge field is believed to be described by a Chern-Simons action in dimension D+1. Since the coefficient of the Chern-Simons action is quantized, it is a topological invariant (i.e. is unchanged under deformations of the Hamiltonian which do not close the gap). I will explain how this invariant can be extracted, in principle, directly from the ground-state wavefunction of a lattice system. This construction also shows that the Chern-Simons invariant can be viewed as a special case of the many-body Berry phase.

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