Infinite coherence time of edge spins in finite-length chains

TL;DR

This paper demonstrates that in finite-length XY spin chains, edge spins can maintain infinite coherence times at specific magnetic fields due to level crossings, with implications for quantum information preservation.

Contribution

It reveals that level crossings in finite chains lead to infinite coherence times of edge spins, extending understanding of zero modes and coherence in quantum spin systems.

Findings

Edge spins remain coherent at level crossings in finite chains.

Coherence time is infinite at specific magnetic fields.

Lower temperatures increase coherence in non-integrable cases.

Abstract

Motivated by the recent observation that exponentially long coherence times can be achieved for edge spins in models with strong zero modes, we study the impact of level crossings in finite-length spin chains on the dynamics of the edge spins. Focussing on the XY spin-1=2 chain with transverse or longitudinal magnetic field, two models relevant to understand recent experimental results on cobalt adatoms, we show that the edge spins can remain coherent for an infinite time even for a finite-length chain if the magnetic field is tuned to a value at which there is a level crossing. Furthermore, we show that the edge spins remain coherent for any initial state for the integrable case of transverse field because all states have level crossings at the same value of the field, while the coherence time is increasingly large for lower temperatures in the case of longitudinal field, which is non-integrable.