Fock space fragmentation in quenches of disordered interacting fermions

Hilbert space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to non-ergodic dynamics and a possible breakdown of the eigenstate thermalization hypothesis. Here, we demonstrate that also in disordered systems, such as the XXZ model with random on-site fields, fragmentation appears as a natural concept offering fresh perspectives, for example, on many-body localization (MBL). Specifically, we split the Fock-space into subspaces, potential-energy shells, which contain the accessible phase space for the relaxation of a quenched initial state. I will show how this concept of fragmentation emerges in the one-dimensional XXZ model
with disorder.