Stretched-Exponential Melting of a Dynamically Frozen State Under Imprinted Phase Noise in the Ising Chain in a Transverse Field

• Main Authors: Roychowdhury, Krishanu, Das, Arnab
• Format: Journal Article
• Language: English
• Published: 22-10-2024
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2409.09128

Eur. Phys. J. B (2024) 97:134 Dynamical freezing is a phenomenon where a set of local observables emerges
as approximate but stable conserved quantities (freezes) under a strong
periodic drive in a closed quantum system. The expectation values of these
emergent conserved quantities exhibit small fluctuations around their
respective initial values. These fluctuations do not grow with time, and their
magnitude can be tuned down sharply by tuning the drive parameters. In this
work, we probe the resilience of dynamical freezing to random perturbations
added to the relative phases between the interfering states (elements of a
natural basis) in the time-evolving wave function after each drive cycle. We
study this in an integrable Ising chain in a time-periodic transverse field.
Our key finding is, that the imprinted phase noise melts the dynamically frozen
state, but the decay is "slow": a stretched-exponential decay rather than an
exponential one. Stretched-exponential decays (also known as Kohlrausch
relaxation) are usually expected in complex systems with time-scale hierarchies
due to strong disorders or other inhomogeneities resulting in jamming,
glassiness, or localization.