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

Abstract

The XXZ spin-half chain has Heisenberg exchange interactions Jz (J⊥ ) in the z (x, y) direction. The modelhas a transition from the spin-fluid phase for −J⊥ < Jz < J⊥ to the Néel phase for Jz > J⊥ > 0. When bondalternation δ is included, the Néel phase transitions to the dimer phase for a finite value of δ. We determine thephase diagram using simple topological indicators related to the polarization of both spins. When a staggeredmagnetic field B is included, a contour plot of these indicators as a function of δ and B determine the amount oftopological quantized spin pumping around closed circuits in the (δ, B) plane.