A dimerized quantum Heisenberg or XY antiferromagnetic chain has a gap in the
spectrum. We show that a weak incommensurate modulation around a dimerized
chain produces a zero temperature quantum critical point. As the
incommensuration wavelength is varied, there is a transition to a modulated
gapless state. The critical behaviour is in the universality class of the
classical commensurate-incommensurate (Pokrovsky-Talapov) transition. An
analogous metal-insulator transition can also take place for an incommensurate
chain.Comment: 5 pages, revtex, no figures, to appear in J. Phys A Letter
