Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field

The XXZ spin-half chain has Heisenberg exchange interactions Jz (J_⊥) in the z $(x,y)$ direction. The model has a transition from the spin-fluid phase for -J_⊥<Jz<J_⊥ to the N\'eel phase for Jz>J_⊥>0. When bond alternation δ is included, the N\'eel phase transitions to the dimer phase for a finite value of δ. 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 δ and B determine the amount of topological quantized spin pumping around closed circuits in the (δ,B) plane.