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

Incommensuration in quantum antiferromagnetic chain