Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems

• URL: http://arxiv.org/abs/2109.01705v3
• Date: Wed, 17 Nov 2021 21:38:44 GMT
• Title: Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
• Authors: Krishnanand Mallayya and Marcos Rigol
• Abstract summary: We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems. We show that the slow thermalizing dynamics is characterized by a rate $propto g2$, which can be accurately determined using a Fermi golden rule (FGR) equation.
• Score: 0.3921666708205728
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form $\hat{H}_0+g\hat{V}$, where $\hat{H}_0$ is nonintegrable and $g\hat{V}$ is a perturbation. We explore the dynamics of far from equilibrium initial states in the thermodynamic limit using a numerical linked cluster expansion (NLCE), and in finite systems with periodic boundaries using exact diagonalization. We argue that generic observables exhibit a two-step relaxation process, with a fast prethermal dynamics followed by a slow thermalizing one, only if the perturbation breaks a conserved quantity of $\hat{H}_0$ and if the value of the conserved quantity in the initial state is $\mathcal{O}(1)$ different from the one after thermalization. We show that the slow thermalizing dynamics is characterized by a rate $\propto g^2$, which can be accurately determined using a Fermi golden rule (FGR) equation. We also show that during such a slow dynamics, observables can be described using projected diagonal and Gibbs ensembles, and we contrast their accuracy.

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