Frank Göhmann, Karol K. Kozlowski, Jesko Sirker, Junji Suzuki
SciPost Phys. 12, 158 (2022) ·
published 12 May 2022

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We present a series representation for the dynamical twopoint 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 longtime largedistance asymptotic behaviour which can be obtained explicitly from a saddlepoint analysis. The spacetime Fourier transform of the twopoint 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 oneparticle, onehole contribution, equivalently interpreted as a twospinon contribution, we obtain an exact and explicit expression in terms of known special functions. For large enough anisotropy, the twospinon contribution carries most of the spectral weight, as can be seen by calculating the fsum rule.
Olivier Babelon, Karol K. Kozlowski, Vincent Pasquier
SciPost Phys. 5, 035 (2018) ·
published 18 October 2018

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We construct a basis of solutions of the scalar $\boldsymbol{ \texttt{t} } \boldsymbol{ \texttt{Q} }$ equation describing the spectrum of the $q$Toda and Toda$_2$ chains by using auxiliary nonlinear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatzlike equations.