Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

TL;DR

This paper presents a theoretical study of heat transport in large-$J$ Heisenberg spin chains, focusing on weak spin-phonon interactions, deriving a microscopic scattering rate, and explaining experimental observations without invoking a spin-Peierls transition.

Contribution

It introduces a rigorous microscopic derivation of spin-phonon scattering in spin chains with weak coupling, avoiding the need for large coupling constants used in previous models.

Findings

The mean-free path shows a temperature dependence consistent with experiments.

The approach explains heat transport without requiring a spin-Peierls transition.

The scattering rate aligns with an intuitive phonon-defect picture.

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.