Detecting topological orders through continuous quantum phase transition

We study a continuous quantum phase transition that breaks a $Z_2$ symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well defined symmetry breaking order parameter. The new critical point arises since the transition not only break the $Z_2$ symmetry, it also changes the topological/quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological/quantum orders in those phases.

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