Stability and fine structure of symmetry-enriched quantum criticality in a spin ladder triangular model

Understand

In this letter, we propose and study a ladder triangular cluster model which possesses a $\mathbb{Z}_2$ symmetry and an anti-unitary $\mathbb{Z}^{\mathbb{T}}_2$ symmetry generated by the spin-flip and complex conjugation, respectively.

• The phase diagram of the model hosts a critical line between a spontaneous symmetry breaking phase and a symmetry protected topological phase.
• Along the critical line, one endpoint exhibits symmetry-enriched Ashkin-Teller universality (SEATU), while other critical points fall into the symmetry-enriched Ising universality (SEIU).
• Both universality classes accommodate symmetry protected degenerate edge modes under open boundary conditions.