Localization-protected quantum order

Many-body localization (MBL) is a dynamical phenomenon which leads to the breakdown of equilibrium statistical mechanics in isolated many-body systems. Such systems never reach local thermal equilibrium, and retain local memory of their initial conditions for infinite times. One can still define a notion of phase structure in these out-of-equilibrium systems. Strikingly, MBL can even enable new kinds of exotic orders that are disallowed in thermal equilibrium – a phenomenon that goes by the name of localization-protected quantum order (LPQO) or eigenstate order.^{[1][2][3][4][5]}