An exactly soluble model describing a spin $S=1\mathrm{}$ antiferromagnetic chain doped with mobile $S=1\mathrm{}/2$ carriers is constructed. In its continuum limit the undoped state is described by three gapless Majorana fermions composing the $\mathrm{SU}\left(2\right)$ triplet. Doping adds a scalar charge field and a singlet Majorana fermion with different velocity. We argue that this mode survives when the Haldane gap is added.

• Received 12 March 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.2116