Fig. 1: Dynamics in the confined Ising chain.
From: Prethermalization in one-dimensional quantum many-body systems with confinement
a Pairs of domain walls, interpreted as mesons, are confined by the longitudinal field. b For weak quantum quenches of the transverse and longitudinal fields the Ising chain exhibits a multi-stage relaxation dynamics. Insets: typical domain wall trajectories in the different dynamical phases. At short times, t < tPreTh ∝ ρ−2h∥ (with ρ the density of mesons) a metastable state arises in which mesons are at rest and well separated. For intermediate times tPreTh < t < tTh, rare events initiate avalanches of scattering processes, leading to prethermal Gibbs ensemble with conserved density of mesons ρ. At late times \(t\, > \,{t}_{{{\mbox{Th}}}}\propto \exp [(...){h}_{\parallel }^{-1}]\), the Schwinger mechanism breaks the meson-number conservation leading to full thermalization. c The meson density ρ, computed with tensor network simulations, relaxes to the analytical prediction (dashed gray lines) of ref. 15 (see also supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.)).
