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arXiv · 2507.12193

Emergent Symmetry and Phase Transitions on the Domain Wall of $\mathbb{Z}_{2}$ Topological Orders

Hong-Hao Song·Chen Peng·Rui-Zhen Huang·Long Zhang
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Abstract

The one-dimensional (1D) domain wall of 2D $\mathbb{Z}_{2}$ topological orders is studied theoretically. The Ising domain wall model is shown to have an emergent SU(2)$_{1}$ conformal symmetry because of a hidden nonsymmorphic octahedral symmetry. While a weak magnetic field is an irrelevant perturbation to the bulk topological orders, it induces a domain wall transition from the Tomonaga-Luttinger liquid to a ferromagnetic order, which spontaneously breaks the anomalous $\mathbb{Z}_{2}$ symmetry and the time-reversal symmetry on the domain wall. Moreover, the gapless domain wall state also realizes a 1D topological quantum critical point between a $\mathbb{Z}_{2}^{T}$-symmetry-protected topological phase and a trivial phase, thus demonstrating the holographic construction of topological transitions.

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Hong-Hao Song, Chen Peng, Rui-Zhen Huang, Long Zhang. 2025-07-16. Emergent Symmetry and Phase Transitions on the Domain Wall of $\mathbb{Z}_{2}$ Topological Orders. https://doi.org/10.1103/z3h7-bptq

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