Twofold twist defect chains at criticality
Abstract
The twofold twist defects in the D (Z_{k}) quantum double model (Abelian topological phase) carry nonAbelian fractional Majoranalike characteristics. We align these twist defects in a line and construct a onedimensional Hamiltonian which only includes the pairwise interaction. For the defect chain with an even number of twist defects, it is equivalent to the Z_{k} 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 Z_{k} 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 KramersWannier duality symmetry in the Z_{k} 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 evendefect chain, the critical points are the same as the Z_{k} clock conformal field theories (CFTs), while for the odddefect chain, when k ≠4 , the critical points correspond to orbifolding a Z_{2} symmetry of CFTs of the evendefect chain. For k =4 case, we numerically observe some similarity to the Z_{4} twist fields in the S U (2_{) 1}/D_{4} orbifold CFT.
 Publication:

Physical Review B
 Pub Date:
 November 2017
 DOI:
 10.1103/PhysRevB.96.205435
 arXiv:
 arXiv:1709.05560
 Bibcode:
 2017PhRvB..96t5435Y
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics
 EPrint:
 18 pages, 15 figures