Symmetry enriched criticality in a spin triangular ladder model

The phase diagram and universality class of a triangular cluster Ising ladder are studied by infinite time-evolving block decimation algorithm. There is a critical line hosting a phase transition between a spontaneous symmetry breaking phase and a non-trivial symmetry protected topological phase. Except an exceptional point, critical physics along the critical line always falls into the topological Ising universality class. By adding an irrelevant boundary perturbation, we further systematically study the topological degeneracy of the critical line and decaying behavior of finite-size energy splitting of edge mode. After introducing a localized correlation length, we propose that the physical quantity draws a hyperfine structure of the topological Ising universality class, which goes beyond both the Landau paradigm and the conformal field theory.