Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

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-average...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Schultzen, Philipp, Titus, Franz, Hainaut, Clément, Geier, Sebastian, Salzinger, Andre, Tebben, Annika, Zürn, Gerhard, Gärttner, Martin, Weidemüller, Matthias
Format: Article
Language:English
Subjects:
Anisotropy
Approximation
Heisenberg theory
Ising model
Robustness (mathematics)
Statistical models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.13314