Entanglement dynamics in confining spin chains

The confinement of elementary excitations induces distinctive features in the non-equilibrium quench dynamics. One of the most remarkable is the suppression of entanglement entropy which in several instances turns out to oscillate rather than grow indefinitely. While the qualitative physical origin of this behavior is clear, till now no quantitative understanding away from the field theory limit was available. Here we investigate this problem in the weak quench limit, when mesons are excited at rest, hindering entropy growth and exhibiting persistent oscillations. We provide analytical predictions of the entire entanglement dynamics based on a Gaussian approximation of the many-body state, which captures numerical data with great accuracy and is further simplified to a semiclassical quasiparticle picture in the regime of weak confinement. Our methods are valid in general and we apply explicitly to two prototypical models: the Ising chain in a tilted field and the experimentally relevant long-range Ising model.