Transition of a $\mathbb{Z}_3$ topologically ordered phase to trivial and critical phases

Understand

Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian.

• We consider topological phase transitions under a deformation such as an effective string tension on a $\mathbb{Z}_3$ topological state.
• This is studied in terms of the gauge-symmetry preserved quantum state renormalization group, first proposed by He, Moradi and Wen [Phys.
• Rev.