  The twofold twist defects in the $D(\mathbb{Z}_k)$ 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 even number of twist defects, it is equivalent to the
$\mathbb{Z}_k$ clock model with periodic boundary condition (up to some phase
factor for boundary term), while for odd number case, it maps to $\mathbb{Z}_k$
clock model with duality twisted boundary condition. At critical point, for
both cases, the twist defect chain enjoys an additional translation symmetry,
which corresponds to the Kramers-Wannier duality symmetry in the $\mathbb{Z}_k$
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 even-defect chain, the critical points are the
same as the $\mathbb{Z}_k$ clock conformal field theories (CFTs), while for
odd-defect chain, when $k\neq 4$, the critical points correspond to orbifolding
a $\mathbb{Z}_2$ symmetry of CFTs of the even-defect chain. For $k=4$ case, we
numerically observe some similarity to the $\mathbb{Z}_4$ twist fields in
$SU(2)_1/D_4$ orbifold CFT.
