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

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.

15 pages, 9 figures

References in corpus (16)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Experimental Observation of a Generalized Gibbs Ensemble
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Generalized Thermalization in an Integrable Lattice System
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Thermalization and light cones in a model with weak integrability breaking
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Typicality of Prethermalization
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Typical relaxation of perturbed quantum many-body systems
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure

Cited by in corpus (3)

• Typicality of nonequilibrium (quasi-)steady currents
• The effect of dressing on thermalization of interacting waves
• Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model