The stability of the magnetization
m=1/3 plateau phase of the
XXZ spin-
21 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 threefold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the
m=1/3 plateau phase to a phase where the spins are polarized along the staggered magnetic field. The
Z3 critical properties of the transition are determined within the bosonization approach.
The XXZ spin-half chain has Heisenberg exchange interactions
Jz $({J}_{\ensuremath{\perp}})$ in the
z (x,y) direction. The model has a transition from the spin-fluid phase for $\ensuremath{-}{J}_{\ensuremath{\perp}}<{J}_{z}<{J}_{\ensuremath{\perp}}$ to the N\'eel phase for ${J}_{z}>{J}_{\ensuremath{\perp}}>0$. When bond alternation $\ensuremath{\delta}$ is included, the N\'eel phase transitions to the dimer phase for a finite value of $\ensuremath{\delta}$. We determine the phase diagram using simple topological indicators related to the polarization of both spins. When a staggered magnetic field
B is included, a contour plot of these indicators as a function of $\ensuremath{\delta}$ and
B determine the amount of topological quantized spin pumping around closed circuits in the $(\ensuremath{\delta},B)$ plane.