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Phase transitions between topologically distinct gapped phases in isotropic spin ladders

Phase transitions between topologically distinct gapped phases in isotropic spin ladders

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide into two topologically distinct classes, and as a consequence, there exist two topologically distinct types …