text: 144,39,984715238422364161,234398193,Hal Tasaki,"Hal Tasaki ""Topological phase transition and Z2 index for S=1 quantum spin chains"" My new paper on #QuantumSpin chains, which contains the first rigorous proof that the AKLT model is in a nontrivial SPT phase. The argument, which I like, is quite pretty. <LINK>",https://arxiv.org/abs/1804.04337,"We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is invariant under smooth deformation. 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. This rigorously establishes that the AKLT model is in a nontrivial symmetry protected topological phase. ","Topological phase transition and $\mathbb{Z}_2$ index for $S=1$ quantum