Aging dynamics in quenched noisy long-range quantum Ising models

Abstract

We consider the $d$-dimensional transverse-field Ising model with power-law interactions $J/r^{d+\sigma }$ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength $\kappa$ and distances longer than $a(J/\kappa {)}^{2/\sigma }$ with $a$ being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent $\theta =1$ and dynamical critical exponent $z=\sigma /2$. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a non-perturbative way. The above scaling regime is governed by a non-equilibrium fixed point dominated by the noise fluctuations.

Accepted version, 11 pages, 5 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Dynamical quantum phase transitions: a review
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation
• Universal post-quench prethermalization at a quantum critical point

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