Spin liquid fingerprints in the thermal transport of a Kitaev-Heisenberg ladder

We identify fingerprints of a proximate quantum spin-liquid (QSL), observable by finite-temperature dynamical thermal transport within a minimal version of the idealized Kitaev model on a two-leg ladder, if subjected to inevitably present Heisenberg couplings. Using exact diagonalization and quantum typicality, we uncover (i) an insulator-conductor crossover induced by fracton recombination at infinitesimal Heisenberg coupling, (ii) low- and high-energy signatures of fractons, which survive far off the pure QSL point, and (iii) a non-monotonous current life-time versus Heisenberg couplings. Guided by perturbation theory, we find (iv) a Kitaev-exchange induced `one-magnon' contribution to the dynamical heat transport in the strong Heisenberg rung limit.