Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime

Abstract

We derive an explicit expression for the leading term in the late-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This expression is valid for all non-zero finite temperatures and for all magnetic fields below the saturation threshold. It is obtained here by means of a straightforward term-by-term analysis of a thermal form factor series, derived in previous work, and demonstrates the usefulness of the latter.

Figures (2)

• Figure 1: Sketch of the hole and particle contours ${\cal C}_h$ and ${\cal C}_p$. The Fermi rapidity $\lambda_F^-$ is located inside ${\cal C}_h$, while $\lambda_F^+$ lies inside ${\cal C}_p$.
• Figure 2: Real part of $\langle \sigma^-_1 \sigma^+_{m+1}(t)\rangle$ as a function of $m$ for $T/J=0.05$, $h/J=0.1$ and $Jt=10$ evaluated numerically and from (\ref{['xxtransasy']}).

Theorems & Definitions (4)

• Theorem
• Lemma
• proof
• proof : Proof of the Theorem