# Preparation of non-ergodic states in quantum spin chains

## TL;DR

This paper investigates the long-time non-ergodic behavior of magnetization in a solvable semi-infinite XY spin chain with an impurity, highlighting the role of localized states and quantum interference in persistent oscillations.

## Contribution

It demonstrates how localized impurity states induce non-ergodic magnetization dynamics and identifies the Rabi frequency as the oscillation frequency of remanent magnetization.

## Key findings

- Localized states are separated from the continuum in certain impurity parameter regions.
- Bound states cause non-ergodic behavior with persistent oscillations.
- Quantum interference between impurity states leads to long-time magnetization oscillations.

## Abstract

We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site magnetization along the chain, focusing on the long-time behavior of the magnetization, which is estimated using the stationary phase method. Localized states are split off from the continuum for some regions of the impurity parameter space. Bound states are essential for the non-ergodic behavior reported here. When two impurity states exist, the quantum interference between them leads to magnetization oscillations which settle over very long times with the absence of damping. The frequency of the remanent oscillation is recognized as being the Rabi frequency of the localized levels.