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## Thermal transport in disordered one-dimensional spin chains

We study a one-dimensional anisotropic XXZ Heisenberg spin-12 chain with weak random fields hizSiz by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First, we reinvestigate the phase diagram of the system in terms of dimensionless disorder γ=h2/J2≪1 and anisotropy parameter Δ=Jz/Jxy, we find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws, and compare it with previously obtained numerical and analytical results. Then we use the diagram technique in terms of plasmon excitations to study the low-temperature (T≪J) behavior of heat conductivity κ and spin conductivity σ in this power-law phase. The obtained Lorentz number L≡κ/σT differs from the value derived earlier by means of the memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.