Topological Tricritical Ising Universality Class in One Dimension

Abstract

Recent advances have revealed that quantum critical universality can be enriched by nontrivial topology. Here we study the tricritical point of the one-dimensional cluster O Brien-Fendley model and show that it realizes a topologically nontrivial tricritical Ising ($\text{TCI}^*$) universality class. The transition shares the local bulk conformal data of ordinary TCI criticality, while realizing a distinct symmetry-enriched topological sector, manifested through a protected twofold degeneracy under open boundary conditions. We further show that TCI criticality admits two spontaneously fixed boundary conditions, realized respectively through symmetry enrichment and boundary renormalization-group flow, which are distinguished by the $\mathbb{Z}_2^T$ charge of the disorder field. Remarkably, we find that the topological twofold degeneracy at the $\text{TCI}^*$ critical point exhibits an exponential energy splitting, in stark contrast to the algebraic splitting at the $\text{Ising}^*$ critical point. These results reveal a symmetry-enriched form of TCI criticality and uncover topologically distinct boundary structures beyond those of the ordinary TCI theory.