  We present a method to calculate the optical conductivity of semi-Dirac and
pseudospin models based on the evaluation of quasiparticle velocity correlators
which also describe the phenomenon of zitterbewegung. Applying this method to
the semi-Dirac model with merging Dirac cones and gapped dice and Lieb lattice
models we find exact analytical expressions for optical longitudinal and Hall
conductivities. For the semi-Dirac model the obtained expressions allow us to
analyze the role of spectrum anisotropy, van Hove singularities and Dirac cones
in longitudinal conductivity. In addition, we predict signatures of topological
phase transition with changing gap parameter in such a system that are
manifested in dc transport at low temperatures. For the dice and Lieb lattices
we emphasize the role of spectral gap, which defines frequency thresholds
related to transitions to and from flat band.
