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

Abstract

We analyze 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.

v2: 13 pages LaTeX, three more figures added, comments added in introduction and discussion

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Cited by in corpus (5)

• Exact real-time longitudinal correlation functions of the massive XXZ chain
• Correlation functions of one-dimensional strongly interacting two-component gases
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime