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We investigate theoretically the spiral staircase Heisenberg spin-$1/2$ladder in the presence of antiferromagnetic long-range spin interactions and auniform magnetic field. As a special case we also consider the Kondo necklacemodel. If the magnetizations of the two chains forming the ladder satisfy acertain resonance condition, involving interchain couplings as perturbations,the system is in a partially gapped magnetic phase hosting excitationscharacterized by fractional spins, whose values can be changed by the magneticfield. We show that these fractional spin excitations can be probed by spincurrents in a transport setup with a spin conductance that reveals thefractionalized spin. In some special cases, the spin conductance reachesuniversal values in units of $(g\mu_B)^2/h$, where $g$ is the $g$-factor,$\mu_B$ the Bohr magneton, and $h$ the Planck constant. We obtain our resultswith the help of bosonization and numerical density matrix renormalizationgroup methods.

Fractional spin excitations and conductance in the spiral staircase Heisenberg ladder