Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

Abstract

The heat transport in a system of $S=1/2$ large-$J$ Heisenberg spin chains, describing closely Sr${}_2$CuO${}_3$ and SrCuO${}_2$ cuprates, is studied theoretically at $T\ll J$ by considering interactions of the bosonized spin excitations with optical phonons and defects. Treating rigorously the multi-boson processes, we derive a microscopic spin-phonon scattering rate that adheres to an intuitive picture of phonons acting as thermally populated defects for the fast spin excitations. The mean-free path of the latter exhibits a distinctive $T$-dependence reflecting a critical nature of spin chains and gives a close description of experiments. By the naturalness criterion of realistically small spin-phonon interaction, 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.

5+ pages main text, 4+ pages supplemental, 4+2 figures, adiabatic approximation to the published version

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• Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Quantum hydrodynamics of spin winding
• Thermal conductivity of local moment models with strong spin-orbit coupling
• Terahertz high-harmonic generation in gapped antiferromagnetic chains
• Low-temperature heat transport of spin-gapped quantum magnets
• Large magnetic thermal conductivity induced by frustration in low-dimensional quantum magnets
• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
• Phonon anomalies and critical scaling in the spin-$1/2$ trimer chain Na${}_2$Cu${}_3$Ge${}_4$O${}_{12}$
• Spin and thermal current scaling at a $Y$-junction of XX spin chains
• Scattering of spinon excitations by potentials in the 1D Heisenberg model