  It is shown that integrability is an accidental property of generic
two-dimensional $O(2)$-symmetric asymptotically-free theories in the regime
where the charge density is much larger than the dynamical scale. We show this
by constructing an infinite tower of higher-spin conserved currents in the most
generic effective Lagrangian at large chemical potential to all orders in
perturbative expansion in the renormalization-group invariant coupling
constant.
