Glassy quantum dynamics of disordered Ising spins

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 $\alpha \ge d$ 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.

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• Ultrafast Many-Body Dynamics in an Ultracold Rydberg-Excited Atomic Mott Insulator
• Many-body radiative decay in strongly interacting Rydberg ensembles
• Observation of anisotropy-independent magnetization dynamics in spatially disordered Heisenberg spin systems
• A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics
• Semiclassical simulations predict glassy dynamics for disordered Heisenberg models
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Dynamics of position disordered Ising spins with a soft-core potential
• Continuously tracked, stable, large excursion trajectories of dipolar coupled nuclear spins
• Effects of critical correlations on quantum percolation in two dimensions