Plateau transitions of spin pump and bulk-edge correspondence

TL;DR

This paper demonstrates quantized plateau transitions in quantum spin chains using a spin pump, linking bulk topological invariants with edge phenomena through a detailed analysis of Berry phases and boundary effects.

Contribution

It introduces a novel spin pump protocol that reveals bulk-edge correspondence in quantum spin chains via topological invariants and boundary spin effects.

Findings

Quantized plateau transitions observed in spin chains with different spins.

Bulk characterized by Chern number related to boundary twist.

Edge effects linked to discontinuities in spin center of mass.

Abstract

Sequential plateau transitions of quantum spin chains ($S$=1,3/2,2 and 3) are demonstrated by a spin pump using dimerization and staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as a time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With open boundary condition, discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk edge correspondence. It requires extra level crossings in the pump as a super-selection rule that is consistent with the Valence Bond Solid (VBS) picture.