Coherent states for [formula omitted]-component fractional quantum Hall systems and their nonlinear sigma models

Abstract

We revise the subject of N-component fractional quantum Hall systems and its field-theoretic description in terms of U(N)-invariant nonlinear sigma models under a group-theoretical perspective. The Berry Lagrangian, which determines the dynamics and encodes the quantum commutation relations for the order parameter, is quantized and the Hilbert space is interpreted in terms of states of N-component composite fermions (M electrons bound to f magnetic flux lines) for fractional filling factor ν=M/f, in accordance with Jain’s picture. An explicit bosonic realization of coherent states on the Grassmannian manifold U(N)/[U(M)×U(N−M)] is provided, which describes coherent excitations of these composite fermions.