Quasi-soliton scattering in quantum spin chains

TL;DR

This paper demonstrates that magnon bound states in quantum spin chains exhibit soliton-like scattering behavior, with measurable displacements upon collision, analyzed through Bethe ansatz and numerical simulations.

Contribution

It introduces a method to construct and analyze localized magnon wave packets in quantum spin chains, revealing soliton-like scattering features and deriving analytic predictions for displacements.

Findings

Magnon bound states display soliton-like scattering displacements.

Analytic phase shift predictions match numerical time evolution results.

TEBD simulations confirm scattering displacements in spin-block states.

Abstract

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The time evolved block decimation (TEBD) algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.