Quantum scars and partial breaking of ergodicity

If we have a well isolated many body quantum system which is time evolving according to its own Hamiltonian, then how should we understand the long time limit of the dynamics? Traditional textbooks on quantum statistical mechanics assume that the system goes to thermal equilibrium at long times, at a temperature set by the energy density of the initial condition. However, at least two exceptions to this paradigm are well known. One exception is integrable systems, which have an extensive number of explicit conservation laws. Another is many body localized systems, which have an extensive number of emergent conservation laws. Both integrable and many body localized systems can evade ergodicity, however for integrable systems it remains unknown whether ergodicity breaking is robust to small perturbations of the Hamiltonian, whereas many body localization has only been proven to exist for strongly disordered spin chains [1]. Do there exist alternative routes to ergodicity breaking, which do not rely on the existence of an extensive number of (explicit or emergent) conservation laws, or on strong disorder?Examples of ergodicity breaking Hamiltonians which are neither integrable nor many body localized have been known in the theory literature for some years. For example,[2] identified a tower of exact non-thermal eigenstates embedded in the spectrum of the (nonintegrable, disorder free) spin-1 AKLT Hamiltonian. Meanwhile, Shiraishi and Mori [3] proposed a generic method by which non-thermal eigenstates could be ‘embedded’into the spectrum of an otherwise thermalizing Hamiltonian. The search for new mechanisms for breaking …