2017/09/16 by Xiongjie Yu, Xiao Chen, Abhishek Roy +1
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Chain (unit) #Combinatorics #Geometry #Hamiltonian (control theory) #Mathematical physics #Mathematics #Orbifold #Physics #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Twist #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.205435
published as Phys. Rev. B 96, 205435 (2017) · 18 pages, 15 figures
arxiv created 2017/09/16 · openalex publication_date 2017/11/27 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The twofold twist defects in the D(ℤk) quantum double model (Abelian topological phase) carry non-Abelian fractional Majorana-like characteristics. We align these twist defects in a line and construct a one-dimensional Hamiltonian which only includes the pairwise interaction. For the defect chain with an even number of twist defects, it is equivalent to the ℤk clock model with a periodic boundary condition (up to some phase factor for the boundary term), while for the odd number case, it maps to the ℤk clock model with a duality twisted boundary condition. At the critical point, for both cases, the twist defect chain enjoys an additional translation symmetry, which corresponds to the Kramers-Wannier duality symmetry in the ℤk clock model and can be generated by a series of braiding operators for twist defects. We further numerically investigate the low energy excitation spectrum for k=3,4,5, and 6. For the even-defect chain, the critical points are the same as the ℤk clock conformal field theories (CFTs), while for the odd-defect chain, when k\ensuremath≠4, the critical points correspond to orbifolding a ℤ2 symmetry of CFTs of the even-defect chain. For k=4 case, we numerically observe some similarity to the ℤ4 twist fields in the SU(2)1/D4 orbifold CFT.