Comment on “Spin Transport Properties of the Quantum One-Dimensional Non-Linear Sigma Model”

In a recent preprint (cond-mat/9905415), Fujimoto has used the Bethe ansatz to compute the finite temperature, zero frequency Drude weight of spin transport in the quantum O(3) non-linear sigma model in a magnetic field H = 0. We show here that, contrary to his claims, the results are in accord with earlier semiclassical results (Sachdev and Damle, Phys. Rev. Lett. 78, 943 (1997)). We also comment on his 1/N expansion, and show that it does not properly describe the long-time correlations. Typeset using REVTEX 1 In a recent preprint 1, Fujimoto has considered non-zero temperature (T) transport in the one-dimensional quantum O(3) non-linear sigma model. He considers the frequency (ω) dependent spin-conductivity, σ(ω), and tests for the possibility that it has a term of the form Re σ(ω) = Kδ(ω) +.... (1) In the presence of a non-zero magnetic field, H = 0, he uses a Bethe ansatz computation to show in the low-temperature limit that K ∼ √ Te −(∆−H)/T, where ∆ is the magnitude of the T = 0 energy gap. Here we will show that, contrary to the claims of Fujimoto 1, this result is in precise accord with earlier semiclassical results 2. For a classical system, the dynamical spin conductivity is given in terms of the the time (t) autocorrelation of the total spin current J(t) as σ(ω) = 1 〈J(t)J(0)〉e