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# Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime

Abstract : We analyse the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obtain the explicit form of the asymptotics of the auto-correlation function.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01413200
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 9 décembre 2016 - 14:46:50
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

### Citation

Maxime Dugave, Frank Göhmann, Karol Kozlowski, Junji Suzuki. Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49 (7), ⟨10.1088/1751-8113/49/7/07LT01⟩. ⟨hal-01413200⟩

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