We present a series representation for the dynamical two-point function of the local spin current for the XXZ chain in the antiferromagnetic massive regime at zero temperature. From this series we can compute the correlation function with very high accuracy up to very long times and large distances. Each term in the series corresponds to the contribution of all scattering states of an even number of excitations. These excitations can be interpreted in terms of an equal number of particles and holes. The lowest term in the series comprises all scattering states of one hole and one particle. This term determines the long-time large-distance asymptotic behaviour which can be obtained explicitly from a saddle-point analysis. The space-time Fourier transform of the two-point function of currents at zero momentum gives the optical spin conductivity of the model. We obtain highly accurate numerical estimates for this quantity by numerically Fourier transforming our data. For the one-particle, one-hole contribution, equivalently interpreted as a two-spinon contribution, we obtain an exact and explicit expression in terms of known special functions. For large enough anisotropy, the two-spinon contribution carries most of the spectral weight, as can be seen by calculating the f-sum rule.
Cited by 4
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Bergische Universität Wuppertal / University of Wuppertal [BUW]
- 2 Université de Lyon / University of Lyon
- 3 Université du Manitoba / University of Manitoba
- 4 静岡大学 / Shizuoka University
- Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- European Research Council [ERC]
- 日本学術振興会 / Japan Society for the Promotion of Science [JSPS]
- Conseil de Recherches en Sciences Naturelles et en Génie / Natural Sciences and Engineering Research Council [NSERC / CRSNG]