A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of $M$ sites with $N$ fermion modes per site, and has a conserved charge $Q$. It has an on-site chemical potential $mu$ with disorder $W$, and an interaction of strength $J$ restricting each fermion to excite two more fermions when moving forward by one site. We show the $N=3$ model with disorder $W=0$ show a Hilbert space fragmentation in all charge $Q$ sectors and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the $N=3$ model exhibits many-body localization (MBL) as $M ightarrowinfty$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests a MBL to quantum chaos crossover as $M/N$ decreases across $1$. At $W=0$, an exactly solvable many-body scar flat band exists in many charge $Q$ sectors, leading to measure nonzero number of quantum scar eigenstates in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows the model is in a breakdown (dielectric) phase when $mu/J1/2$). The breakdown is local when $M/Ngg1$, and is global when $M/Nll 1$.