Topological phase transition and $\mathbb{Z}_2$ index for $S=1$ quantum spin chains

Hal Tasaki

Published 2018-04-12Version 1

We study $S=1$ quantum spin systems on the infinite chain with short range interactions which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for a gapped unique ground state, and prove that it is invariant under smooth deformation of the ground state. By using the index, we provide the first rigorous proof of the existence of a "topological" phase transition, which cannot be characterized by any conventional order parameters, between the AKLT ground state and trivial ground states.