Two-dimensional quantum breakdown model with Krylov subspace many-body localization

We propose a two-dimensional (2d) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set of subsystem symmetries, and has a strong fragmentation into Krylov subspaces in each symmetry sector. The Hamiltonian in each Krylov subspace maps to a single-particle problem in a Cayley tree-like graph. At zero disorder, the Krylov subspaces exhibit either (possible) integrable features, or quantum chaos with quantum scar states showing irregular energy and degeneracy patterns. At nonzero disorders, they enter a 2d many-body localization (MBL) phase beyond certain disorder strength $W_*$, as indicated by Poisson level spacing statistics and entanglement entropy growing as $\log t$ with time $t$. Our theoretical arguments suggest $W_*$ is finite or zero for boson number $N_b\lesssim L^\gamma/\log L$ ($1/2\le \gamma \le 1$) as system size $L\rightarrow\infty$. This gives a more stringent condition for MBL than that in the 1d quantum breakdown models. This model reveals the possibility of MBL in systems of quantum particles interacting with classical degrees of freedom.