# Real-time scattering of interacting quasiparticles in quantum spin chains

## TL;DR

This paper introduces a tensor network-based method to generate and analyze localized quasiparticle excitations in quantum spin chains, enabling the study of scattering, phase shifts, and impurity interactions in real-time.

## Contribution

It presents a novel approach to create and manipulate localized quasiparticles in strongly-correlated spin chains using tensor networks and variational principles.

## Key findings

- Wavepackets propagate almost dispersionless
- Phase shifts can be extracted from scattering data
- Reflection and transmission coefficients are characterized

## Abstract

We develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wavepackets propagate almost dispersionless. The time-dependent variational principle is used to scatter two such wavepackets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wavepacket impinging on an impurity.