# Contrast Analysis on Spin Transport of Multi-Periodic Exotic States in the XXZ Chain

## TL;DR

This paper studies how spins move in a quantum system using two special initial states and finds differences in transport behavior based on system parameters.

## Contribution

The study introduces a contrast method to analyze spin transport in exotic initial states and identifies distinct transport behaviors.

## Key findings

- Spin transport is impeded and varies between multi-periodic domain-wall and spin-helix states as anisotropy increases.
- Contrast methods effectively extract scaling exponents for exotic states within experimentally accessible timescales.

## Abstract

Quantum spin transport in integrable systems reveals a rich nonequilibrium phenomena that challenges the conventional hydrodynamic framework. Recent advances in ultracold atom experiments with state preparation and single-site addressing have enabled the understanding of this anomalous behavior. Particularly, the full universality characterization of exotic initial states, as well as their measurement representation, remain unknown. By employing tensor network and contrast methods, we systematically investigate spin transport in the quantum XXZ spin chain and extract dynamical scaling exponents emerging from two paradigmatic and experimentally attainable initial states, i.e., multi-periodic domain-wall (MPDW) and spin-helix (SH) states. Our results using different values of anisotropic parameters Δ∈[0,1.2] demonstrate the evident impeded transport and the difference between the two states with increasing Δ values. Large-scale and consistent simulations confirm the contrast method as a viable scaling extraction approach for exotic states with periodicity within experimentally accessible timescales. Our work establishes a foundation for studying initial memory and the corresponding relations of emergent transport behavior in nonequilibrium quantum systems, opening avenues for the identification of their unique universality classes.