Heat transport in spin chains with weak spin-phonon coupling

We propose that the heat conductivity by 1D spin excitations in $S=1/2$ Heisenberg spin chains can be quantitatively described within the bosonization framework, in which large-momentum scattering of spin excitations is due to optical phonons with the spin-phonon couplings that are well within the physical bounds. Our theory provides an excellent fit to the data from the systematic experimental thermal conductivity studies in the high-quality single-crystalline large-$J$ spin-chain cuprates that have recently become available. Our description of the spin-phonon scattering is also in accord with a physically intuitive picture of phonons playing the role of thermally-populated weak impurities for the fast spin excitations. Our approach stands out from previous considerations that require large coupling constants to explain the data and thus imply a spin-Peierls transition, absent in real materials.