  The optical conductivities of two one-dimensional narrow-gap semiconductors,
anticrossing quantum Hall edge states and carbon nanotubes, are studied using
bosonization method. A lowest order renormalization group analysis indicates
that the bare band gap can be treated perturbatively at high
frequency/temperature. At very low energy scale the optical conductivity is
dominated by the excitonic contribution, while at temperature higher than a
crossover temperature the excitonic features are eliminated by thermal
fluctuations. In case of carbon nanotubes the crossover temperature scale is
estimated to be 300 K.
