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This work proposes a closed formula for the leading term of the long-distanceand large-time asymptotics in a cone of the space-like regime for thetransverse dynamical two-point functions of the XXZ spin 1/2 chain at finitetemperatures. The result follows from a simple analysis of the thermal formfactor series for dynamical correlation functions. The leading asymptotics weobtain are driven by the Bethe Ansatz data associated with the firstsub-leading Eigenvalue of the quantum transfer matrix.

Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain