Holons on a meandering stripe: Quantum numbers

We attempt to access the regime of strong coupling between charge carriers and transverse dynamics of an isolated conducting “stripe,” such as those found in cuprate superconductors. A stripe is modeled as a partially doped domain wall in an antiferromagnet $\left(\mathrm{AF}\right),$ introduced in the context of two different models: the $t-J$ model with strong Ising anisotropy, and the Hubbard model in the Hartree-Fock approximation. The domain walls with a given linear charge density are supported artificially by boundary conditions. In both models we find a regime of parameters where doped holes lose their spin and become holons (charge $Q=1,$ spin $S_3=0),$ which can move along the stripe without frustrating AF environment. One aspect in which the holons on the AF domain wall differ from those in an ordinary one-dimensional electron gas is their transverse degree of freedom: a mobile holon always resides on a transverse kink (or antikink) of the domain wall. This gives rise to two holon flavors and to a strong coupling between doped charges and transverse fluctuations of a stripe.