Thermalization and hydrodynamic long-time tails in a Floquet system

• URL: http://arxiv.org/abs/2410.16182v2
• Date: Thu, 19 Dec 2024 12:34:01 GMT
• Title: Thermalization and hydrodynamic long-time tails in a Floquet system
• Authors: Anne Matthies, Nicolas Dannenfeld, Silvia Pappalardi, Achim Rosch,
• Abstract summary: We investigate whether classical hydrodynamic field theories can predict the long-time dynamics of many-particle quantum systems. Based on a field theoretical analysis and symmetry arguments, we map each operator in the spin model to corresponding fields in hydrodynamics. We show that all operators not protected by hydrodynamics decay exponentially and investigate a selected set of slowly decaying operators.
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• Abstract: We systematically investigate whether classical hydrodynamic field theories can predict the long-time dynamics of many-particle quantum systems. As an example, we investigate numerically and analytically the time evolution of a chain of spins (or qubits) subject to a stroboscopic dynamics. The time evolution is implemented by a sequence of local and nearest-neighbor gates which conserve the total magnetization. The long-time dynamics of such a system is believed to be describable by a hydrodynamics field theory, which, importantly, includes the effect of noise. Based on a field theoretical analysis and symmetry arguments, we map each operator in the spin model to corresponding fields in hydrodynamics. This allows us to predict which expectation values decay exponentially, and which of them decay with a hydrodynamics long-time tail. We illustrate these findings by studying the time evolution of all 255 Hermitian operators which can be defined on four neighboring sites. We show that all operators not protected by hydrodynamics decay exponentially and investigate a selected set of slowly decaying operators.

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