Glassy quantum dynamics of disordered Ising spins

TL;DR

This paper investigates the quantum dynamics of disordered Ising spins with long-range interactions, revealing glassy behavior characterized by stretched exponential decay of magnetization and purity, and identifying the underlying mechanisms.

Contribution

It analytically derives the stretched exponential decay in the quantum Ising model with disorder and long-range interactions, extending classical glassy dynamics to quantum systems.

Findings

Global magnetization decays as a stretched exponential with exponent d/α.

Glassy behavior persists for finite sizes and strong disorder.

Dephasing between disordered pairs causes relaxation, entanglement builds up from many-body interactions.

Abstract

We study the out-of-equilibrium dynamics in the quantum Ising model with power-law interactions and positional disorder. For arbitrary dimension $d$ and interaction range $\alpha \geq d$ we analytically find a stretched exponential decay of the global magnetization and ensemble-averaged single-spin purity with a stretch-power $\beta = d/\alpha$ in the thermodynamic limit. Numerically, we confirm that glassy behavior persists for finite system sizes and sufficiently strong disorder. We identify dephasing between disordered coherent pairs as the main mechanism leading to a relaxation of global magnetization, whereas genuine many-body interactions lead to a loss of single-spin purity which signifies the build-up of entanglement. The emergence of glassy dynamics in the quantum Ising model extends prior findings in classical and open quantum systems, where the stretched exponential law is explained by a scale-invariant distribution of time scales, to both integrable and non-integrable quantum systems.