We study the one-dimensional $t-J-J^{\prime }$-model in the limit of small hole doping x and small $J/t,$ $J^{\prime }/t.\mathrm{}$ Special emphasis is put on the regime $J^{\prime }/J\approx 0.5,$ where a spin gap is present at small doping and the undoped spin chain is strongly dimerized. Using a perturbative approach and Luttinger liquid arguments, we demonstrate for this nonintegrable class of models that the charge degrees of freedom behave as noninteracting spinless solitons in the dilute hole limit. Our approach is also used to evaluate the energy and mass renormalization of a single hole. Interestingly, the corrections of these quantities are in powers of $\sqrt{J/t}.$ At $J^{\prime }/J=0.5\mathrm{}$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.

• Received 11 September 2003

DOI:https://doi.org/10.1103/PhysRevB.69.094419