Relaxation dynamics in an isolated long-range Ising chain

TL;DR

This paper investigates how long-range interactions in an isolated ion chain influence the relaxation and coherence dynamics of spins, revealing that traditional truncated models fail to capture these effects.

Contribution

It demonstrates the importance of genuine long-range interactions in quantum relaxation dynamics, challenging conventional truncated models and exploring the impact of interaction range.

Findings

Quantum coherence rapidly decreases and vanishes in steady state.

Truncated models cannot replicate the relaxation dynamics.

Longer interaction ranges lead to faster relaxation but longer times near infinite range.

Abstract

We consider a chain of trapped ions to interact with each other via long-range interactions. This system can be used to simulate the long-range Ising model. We study the dynamics of quantum coherence of a single spin in the chain, where the spins are initially prepared in their upper states. The relaxation dynamics exhibits due to the genuine long-range interaction. The degree of quantum coherence of a single spin rapidly decreases and vanishes in the steady state. However, our numerical result suggests that the conventional spin chain model, which truncates the interactions between the distant spins, cannot show the relaxation dynamics. This implies that the usual truncation in approximating the long-range interaction is not applicable to describing the non-equilibrium dynamics. The effect of the interaction range on the relaxation dynamics is studied. The higher relaxation rate will show if a system has a longer range of interaction. However, it takes a longer relaxation time in the vicinity of infinite interaction range. We also examine the dynamics of quantum coherence of a block of spins. Our result may shed light on the relationship between long-range interaction and the coherence dynamics of a quantum many-body system.