Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

TL;DR

This study uses semiclassical simulations to demonstrate that disordered Heisenberg models exhibit glassy dynamics, with relaxation behaviors similar to the Ising limit, regardless of Hamiltonian symmetry.

Contribution

It provides the first systematic numerical evidence that glassy dynamics are prevalent in disordered quantum spin systems across different Hamiltonian symmetries.

Findings

Glassy behavior observed in magnetization and spin purity.

Stretch power close to Ising limit across scenarios.

Glassy relaxation is independent of Hamiltonian symmetry.

Abstract

We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with $1/r^6$ power-law interactions and positional disorder. Using the semi-classical discrete truncated Wigner approximation (dTWA) method, we investigate the time evolution of the magnetization and ensemble-averaged single-spin purity for a strongly disordered system after initializing the system in an out-of-equilibrium state. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian. Furthermore, a systematic analysis allows us to quantitatively show that, for all the scenarios considered, the stretch power lies close to the one analytically obtained in the Ising limit. This indicates that glassy relaxation behavior occurs widely in disordered quantum spin systems, independent of the particular symmetries and integrability of the Hamiltonian.