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 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 delocalization (MBdL). 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. In this construction, dynamical observables reflect properties of the shell geometry, e.g., the drastic sample-to-sample fluctuations observed in the weak disorder regime, $W<W_c$, represent fluctuations of the mass of the shell. Upon crossing over from weak to strong disorder, $W>W_c$, the potential-energy shell decays into fragments; we argue that, unlike percolation, fragmentation is a strong-coupling scenario with turn-around flow: $W_c(L)$ diverges with increasing system size. We conjecture that the slowing down of the relaxation dynamics reported in traditional MBdL studies is (essentially) a manifestation of Fock-space fragmentation introduced here.