  We briefly discuss our recent field-theoretic study of polyelectrolyte
complexation, which occurs in solutions of two oppositely charged
polyelectrolytes. Charged systems require theoretical methods beyond the
mean-field (or self-consistent field) approximation; indeed, mean-field theory
is qualitatively incorrect for such polyelectrolyte solutions. Both analytical
(one-loop) and numerical (complex Langevin) methods to account for charge
correlations are discussed. In particular, the first application of
field-theoretic simulations to polyelectrolyte systems is reported. The
polyelectrolyte charge-charge correlation length and a phase diagram are
provided; effects of charge redistribution are qualitatively explored.
