  We revisit the problem of a single quantum impurity on the edge of a
two-dimensional time-reversal invariant topological insulator and show that the
zero temperature phase diagram contains a large local moment region for
antiferromagnetic Kondo coupling which was missed by previous poor man's
scaling treatments. The combination of an exact solution at the so-called
decoupling point and a renormalization group analysis \`a la
Anderson-Yuval-Hamann allows us to access the regime of strong
electron-electron interactions on the edge and strong Kondo coupling. We apply
similar methods to the problem of a regular one-dimensional array of quantum
impurities interacting with the edge liquid. When the edge electrons are at
half-filling with respect to the impurity lattice, the system remains gapless
unless the Luttinger parameter of the edge is less than 1/2, in which case
two-particle backscattering effects drive the system to a gapped phase with
long-range Ising antiferromagnetic order. This is in marked contrast with the
gapped disordered ground state of the ordinary half-filled one-dimensional
Kondo lattice.
