Quantum Fragmentation in the Extended Quantum Breakdown Model

We introduced a 1D lattice model comprising a fermion and spin degrees of freedom per site, in which the fermions have a hopping and a spatially asymmetric breakdown-type interaction with the spins. The model features a conserved fermion number, dividing the Hilbert space into symmetry sectors. In the absence of a magnetic field, the symmetry sectors further fragment into extensive number of Krylov subspaces and degeneracies, resulting non-thermalization. The root states that generate the Krylov subspaces are entangled states, which indicates that the system is quantum fragmented. With the introduction of a magnetic field, most of the Krylov subspaces merge together, and the model becomes chaotic.