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

This work proposes a closed formula for the leading term of the long-distance and large-time asymptotics in a cone of the space-like regime for the transverse dynamical two-point functions of the XXZ spin 1/2 chain at finite temperatures. The result follows from a simple analysis of the thermal form factor series for dynamical correlation functions. The leading asymptotics we obtain are driven by the Bethe Ansatz data associated with the first sub-leading Eigenvalue of the quantum transfer matrix.