Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime

TL;DR

This paper computes dynamical spin-spin correlation functions for the gapless anisotropic Heisenberg chain using exact determinant form factors, including complex states, and compares results with known formulas and conformal field theory predictions.

Contribution

It introduces modified determinant representations for form factors with string solutions and provides high-precision sum rule saturation in the gapless regime.

Findings

High-precision sum rule saturation achieved

Comparison with exact zero-field correlation functions validated

Asymptotic behavior matches conformal field theory predictions

Abstract

We compute all dynamical spin-spin correlation functions for the spin-1/2 $XXZ$ anisotropic Heisenberg model in the gapless antiferromagnetic regime, using numerical sums of exact determinant representations for form factors of spin operators on the lattice. Contributions from intermediate states containing many particles and string (bound) states are included. We present modified determinant representations for the form factors valid in the general case with string solutions to the Bethe equations. Our results are such that the available sum rules are saturated to high precision. We Fourier transform our results back to real space, allowing us in particular to make a comparison with known exact formulas for equal-time correlation functions for small separations in zero field, and with predictions for the zero-field asymptotics from conformal field theory.