Emergent Symmetry and Phase Transitions on the Domain Wall of ${\mathbb{Z}}_2$ Topological Orders

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.

Main text: 5.5 pages, 4 figures; Appendices: 8.5 pages, 4 figures

References in corpus (7)

• The ITensor Software Library for Tensor Network Calculations
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Topological boundary conditions in abelian Chern-Simons theory
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Emergent SU(2)${}_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction