Nonthermal states in nonintegrable magnetic models*

There is a new paradigm emerging for quantum systems: those which are nonintegrable but nevertheless possess nonthermal states embedded throughout their many-body spectrum (whose number is polynomial in the system size). The presence of such states violates a strong version of the eigenstate thermalization hypothesis, and the behaviour expected for generic nonintegrable systems, such as thermalization, can be broken. Why such nonthermal states appear in certain models is currently not understood, although recent works have drawn analogies with the physics of "quantum scars". We show that nonthermal states, extending far into the many-body spectrum, can arise in simple magnetic (continuum and lattice) models that exhibit confinement and the associated formation of "meson-like" excitations. As a result, certain quenches in these models do not lead to thermalization and the nonequilibrium dynamics of local observables can show persistent, long-lived oscillations.