  The harmonic Dirichlet space $\cal{D} (\mathbb{T})$ is the Hilbert space of
functions $f \in L^2(\mathbb{T})$ such that $$\|f\|_{\cal{D} (\mathbb{T})}^2 :=
\sum_{n\in\mathbb{Z}} (1+|n|)|\hat{f}(n)|^2 < \infty.$$ We give sufficient
conditions for $f$ to be cyclic in $\cal{D} (\mathbb{T})$, in other words, for
$\{\zeta ^nf(\zeta):\ n\geq 0\}$ to span a dense subspace of $\cal{D}
(\mathbb{T})$.
