Magnetic quantum oscillations and multiple holon pockets in the underdoped cuprate YBa2Cu3O6+y

We show that lightly doped YBa2Cu3O6+y has multiple holon pockets with different areas, which lead to multiple frequencies of magnetic quantum oscillations. Using neutron-scattering data on incommensurate spin ordering we determine these areas, which yields frequencies in good agreement with experiments. Divergence of the effective mass observed in magnetic quantum oscillations indicates a quantum phase transition at the oxygen content y approximate to 0.48. We argue that the transition is the onset of quasistatic incommensurate magnetic order predicted by theory and observed in neutron scattering.