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

TL;DR

This paper investigates the long-time, large-distance behavior of correlation functions in the Heisenberg-Ising chain's easy-axis regime, revealing wave front propagation and form factor contributions.

Contribution

It provides an explicit saddle-point analysis of the two-spinon form factor expansion, identifying wave front velocities and asymptotic behavior.

Findings

Wave front propagates at maximal group velocity $v_{c_1}$

Precursor wave runs ahead at velocity $v_{c_2}$

Explicit asymptotics for auto-correlation functions obtained

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.