Z_3 Quantum Criticality in a spin-1/2 chain model

The stability of the magnetization $m=1\mathrm{/}3$ plateau phase of the XXZ spin-1/2 Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional XY model in a three-fold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1\mathrm{/}3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The Z${}_3$ critical properties of the transition are determined within the bosonization approach.