Coherent states for NN-component fractional quantum Hall systems and their nonlinear sigma models

We revise the subject of NN-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 NN-component composite fermions (MM electrons bound to ff magnetic flux lines) for fractional filling factor ν=M/fν=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.