Transition rates via Bethe ansatz for the spin-1/2 Heisenberg chain

TL;DR

This paper employs the Bethe ansatz to compute transition rates for the spin-1/2 Heisenberg chain, providing numerical evaluations of dynamic spin structure factors at zero temperature.

Contribution

It introduces a method to calculate transition rates using determinantal representations for Bethe wave functions, enabling efficient numerical analysis.

Findings

Calculated transition rates for spin fluctuations under magnetic fields.

Numerical evaluation of dynamic spin structure factors at zero temperature.

Demonstrated the applicability of Bethe ansatz to dynamic correlation functions.

Abstract

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z_1,...,z_r of the Bethe ansatz equations, the size of the determinants is of order r x r. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.