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 breaks the $Z_2$ symmetry, it also changes the topological or 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 or quantum orders in those phases.

• Received 13 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.026802