# Confinement in the three-state Potts quantum spin chain in extreme ferromagnetic limit

## TL;DR

This paper studies the three-state Potts quantum spin chain's dynamics in a ferromagnetic limit, revealing resonant excitations and post-quench evolution through a perturbative approach.

## Contribution

It introduces a perturbative method to analyze the Potts model's dynamics, capturing phenomena beyond previous methods, especially in the oblique quench regime.

## Key findings

- Analytic prediction of post-quench time evolution.
- Identification of resonant excitations near stability thresholds.
- Excellent agreement between analytical results and numerical simulations.

## Abstract

We investigate the dynamics of the three-state Potts quantum spin chain in the extreme ferromagnetic limit using a perturbative expansion in the transverse magnetic field. We demonstrate that a perturbative approach provides access to important features beyond the reach of previous studies, most notably the description of resonant excitations and the analytic prediction of post-quench time evolution. A central focus is the oblique quench regime - a feature unique to the Potts model with no Ising counterpart - in which unconfined kink excitations hybridise with the two-kink bound states. We provide a detailed examination of the analytic structure of the two-kink scattering amplitude, tracing the transformation of stable excitations into resonances near stability thresholds. Our analytical results for the excitation spectra and magnetisation dynamics show excellent agreement with numerical simulations of non-equilibrium dynamics.