Spin conductivity of the XXZ chain in the antiferromagnetic massive regime

Abstract

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.

arXiv comment30 pages; v2: typos corrected, some points clarified, Fig. 1 updated, following the referees' suggestions introduction and summary sections have been considerably extended to give more space to background citations; v3 a typo in equation (B.27) corrected

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• Power-law decay of correlations after a global quench in the massive XXZ chain
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• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain