Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $σ$-model

Details Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $σ$-model Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $σ$-model

1996-10-15

arxiv.org/abs/cond-mat/9610115v1

Physical Review Letters, 78, 943 (1997)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages including 3 eps-figures, Revtex

Scientific paper

10.1103/PhysRevLett.78.943

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $O(3)$ non-linear $\sigma$-model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.

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