  In a magnetic field two-dimensional (2d) electron systems host, with quenched
kinetic energy, a variety of many-body correlation phenomena, such as
interaction-driven new states and associated collective excitations over them.
In a magnetic field the two-body operators pertinent to the 2d Coulomb
interaction obey a crossing relation, with which the Coulomb interaction is
also cast into the form of manifest exchange interaction. It is shown that
active use of this direct/exchange duality of the interaction allows one to
develop, within the framework of the single-mode approximation, a new efficient
algorithm for handling a wide class of collective excitations. The utility of
our algorithm is demonstrated by studying some examples of inter- and
intra-Landau-level collective excitations in graphene and in conventional
electron systems.
