Unambiguous Experimental Verification of Linear-in-Temperature Spinon Thermal Conductivity in an Antiferromagnetic Heisenberg Chain

The everlasting interest in spin chains is mostly rooted in the fact that they generally allow for comparisons between theory and experiment with remarkable accuracy, especially for exactly solvable models. A notable example is the spin-1/2 antiferromagnetic Heisenberg chain (AFHC), which can be well described by the Tomonaga-Luttinger liquid theory and exhibits fractionalized spinon excitations with distinct thermodynamic and spectroscopic experimental signatures consistent with theoretical predictions. A missing piece, however, is the lack of a comprehensive understanding of the spinon heat transport in AFHC systems, due to difficulties in its experimental evaluation against the backdrop of other heat carriers and complex scattering processes. Here we address this situation by performing ultralow-temperature thermal conductivity measurements on a nearly ideal spin-1/2 AFHC system copper benzoate Cu(C_{6}H_{5}COO)_{2}·3H_{2}O, whose field-dependent spin excitation gap enables a reliable extraction of the spinon thermal conductivity κ_{s} at zero field. κ_{s} was found to exhibit a linear temperature dependence κ_{s}∼T at low temperatures, with κ_{s}/T as large as 1.70 mW cm^{-1} K^{-2}, followed by a precipitate decline below ∼0.3 K. The observed κ_{s}∼T clarifies the discrepancies between various spin chain systems and serves as a benchmark for one-dimensional spinon heat transport in the low-temperature limit. The abrupt loss of κ_{s} with no corresponding anomaly in the specific heat is discussed in the context of many-body localization.