# Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory

## TL;DR

This paper validates a semi-semiclassical method for describing spin fluctuations after quantum quenches in the S=1 Haldane chain, showing it agrees well with TEBD simulations and improves upon standard semiclassical approaches.

## Contribution

The paper introduces and validates a hybrid semi-semiclassical approach that accurately captures quantum quench dynamics in the S=1 Haldane chain, surpassing traditional semiclassical methods.

## Key findings

- Semi-semiclassical method matches TEBD results.
- Standard semiclassical approach fails to describe dynamics.
- Full scattering matrix improves predictive accuracy.

## Abstract

We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum mechanically. We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry. We show that while the standard semiclassical approach using the universal low energy scattering matrix cannot describe the dynamics, the hybrid semiclassical method based on the full scattering matrix gives excellent agreement with the first principles TEBD simulation.